From 8f162cb7c4f3a6edaff7c1ab756538093fd76bbf Mon Sep 17 00:00:00 2001
From: Jacob Zhong <cmpute@qq.com>
Date: Tue, 26 Apr 2022 04:32:21 -0400
Subject: [PATCH] Adapt to PreInv

---
 ROADMAP.md                |    4 +-
 examples/divisor_sigma.rs |    6 +
 examples/prime_omega.rs   |    5 +
 src/buffer.rs             |   10 +-
 src/factor.rs             |    4 +-
 src/integer.rs            |    2 +
 src/nt_funcs.rs           |  101 +-
 src/tables.rs             | 3084 +++++++++++++------------------------
 src/traits.rs             |    7 +-
 9 files changed, 1127 insertions(+), 2096 deletions(-)
 create mode 100644 examples/divisor_sigma.rs
 create mode 100644 examples/prime_omega.rs

diff --git a/ROADMAP.md b/ROADMAP.md
index 3a57797..cf82539 100644
--- a/ROADMAP.md
+++ b/ROADMAP.md
@@ -2,7 +2,6 @@
 - Implement factorization for Gaussian integers (and other quadratic integers?)
 - Implement a wrapper supporting fast modular arithmetics and use it to speed up is_prime64 and factors64
 - Implement SIQS
-- Add benchmarks for factorization & primality test (ref: SageMath benchmark tests)
 - Euler totient
 
 # Roadmap for v1
@@ -15,3 +14,6 @@
 - Support `rug` and `ibig` as backend
 - Support `rug` & `primal` or `primesieve-sys` as PrimeBuffer backend
 - Support async and multi-thread
+
+# Not in plan
+- Support number field sieve factorization (this is efficient only for very larg numbers)
diff --git a/examples/divisor_sigma.rs b/examples/divisor_sigma.rs
new file mode 100644
index 0000000..69d8be3
--- /dev/null
+++ b/examples/divisor_sigma.rs
@@ -0,0 +1,6 @@
+// https://en.wikipedia.org/wiki/Divisor_function
+// TODO(v0.3.2): implement divisor sigma as example for factorization
+
+fn main() {
+    println!("nothing here")
+}
diff --git a/examples/prime_omega.rs b/examples/prime_omega.rs
new file mode 100644
index 0000000..2844c0b
--- /dev/null
+++ b/examples/prime_omega.rs
@@ -0,0 +1,5 @@
+// https://en.wikipedia.org/wiki/Prime_omega_function
+
+fn main() {
+    unimplemented!()
+}
\ No newline at end of file
diff --git a/src/buffer.rs b/src/buffer.rs
index 2189234..9707f33 100644
--- a/src/buffer.rs
+++ b/src/buffer.rs
@@ -12,7 +12,7 @@
 
 use crate::factor::{pollard_rho, trial_division};
 use crate::nt_funcs::{
-    factorize64, factors, is_prime64, next_prime, nth_prime_bounds, nth_prime_est, prev_prime,
+    factorize128, factors, is_prime64, next_prime, nth_prime_bounds, nth_prime_est, prev_prime,
 };
 use crate::primality::{PrimalityBase, PrimalityRefBase};
 use crate::tables::{SMALL_PRIMES, SMALL_PRIMES_NEXT};
@@ -123,11 +123,11 @@ pub trait PrimeBufferExt: for<'a> PrimeBuffer<'a> {
     where
         for<'r> &'r T: PrimalityRefBase<T>,
     {
-        // shortcut if the target is in u64 range
-        if let Some(x) = target.to_u64() {
-            return Ok(factorize64(x)
+        // shortcut if the target is in u128 range
+        if let Some(x) = target.to_u128() {
+            return Ok(factorize128(x)
                 .into_iter()
-                .map(|(k, v)| (T::from_u64(k).unwrap(), v))
+                .map(|(k, v)| (T::from_u128(k).unwrap(), v))
                 .collect());
         }
         let config = config.unwrap_or(FactorizationConfig::default());
diff --git a/src/factor.rs b/src/factor.rs
index 7fce830..62de154 100644
--- a/src/factor.rs
+++ b/src/factor.rs
@@ -11,6 +11,8 @@ use std::collections::BTreeMap;
 /// The target is guaranteed fully factored only if bound * bound > target, where bound = max(primes).
 /// The parameter limit additionally sets the maximum of primes to be tried.
 /// The residual will be Ok(1) or Ok(p) if fully factored.
+/// 
+/// TODO: implement fast check for small primes with BigInts in the precomputed table, and skip them in this function
 pub fn trial_division<
     I: Iterator<Item = u64>,
     T: Integer + Clone + Roots + NumRef + FromPrimitive,
@@ -85,7 +87,7 @@ where
             return None;
         }
 
-        // FIXME: optimize abs_diff for montgomery form
+        // FIXME: optimize abs_diff for montgomery form if we are going to use the abs_diff in the std lib
         let diff = if b > a { &b - &a } else { &a - &b }; // abs_diff
         let d = diff.gcd(target);
         if d > T::one() && &d < target {
diff --git a/src/integer.rs b/src/integer.rs
index 49d959e..8d256ef 100644
--- a/src/integer.rs
+++ b/src/integer.rs
@@ -59,6 +59,8 @@ macro_rules! impl_exactroot_prim {
             }
         }
     )*};
+    // TODO: it might worth use QUAD_RESIDUE and CUBIC_RESIDUE for large size
+    //       primitive integers, need benchmark
 }
 impl_exactroot_prim!(u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize);
 
diff --git a/src/nt_funcs.rs b/src/nt_funcs.rs
index ed5b284..00477ea 100644
--- a/src/nt_funcs.rs
+++ b/src/nt_funcs.rs
@@ -15,15 +15,17 @@ use crate::buffer::{NaiveBuffer, PrimeBufferExt};
 use crate::mint::Mint;
 use crate::factor::{pollard_rho, squfof};
 use crate::primality::{PrimalityBase, PrimalityRefBase};
-use crate::tables::{MOEBIUS_ODD, SMALL_PRIMES, SMALL_PRIMES_NEXT, WHEEL_NEXT, WHEEL_PREV, WHEEL_SIZE};
+use crate::tables::{MOEBIUS_ODD, SMALL_PRIMES, WHEEL_NEXT, WHEEL_PREV, WHEEL_SIZE};
 #[cfg(feature = "big-table")]
-use crate::tables::{SMALL_PRIMES_INV, SMALL_PRIMES_INVLIM, ZETA_LOG_TABLE};
+use crate::tables::{SMALL_PRIMES_INV, ZETA_LOG_TABLE, SMALL_PRIMES_NEXT};
 use crate::traits::{FactorizationConfig, Primality, PrimalityTestConfig, PrimalityUtils};
 use crate::RandPrime;
 #[cfg(feature = "num-bigint")]
 use num_bigint::{BigUint, RandBigInt};
 use num_integer::Roots;
 use num_modular::{ModularCoreOps, MontgomeryInt, ModularInteger};
+#[cfg(feature = "num-bigint")]
+use num_modular::DivExact;
 use num_traits::{CheckedAdd, FromPrimitive, Num, RefNum, ToPrimitive};
 use rand::{random, Rng};
 use std::collections::BTreeMap;
@@ -49,6 +51,7 @@ pub fn is_prime64(target: u64) -> bool {
         return SMALL_PRIMES.binary_search(&u).is_ok();
     } else {
         // check remainder against the wheel table
+        // this step eliminates any number that is not coprime to WHEEL_SIZE
         let pos = (target % WHEEL_SIZE as u64) as usize;
         if pos == 0 || WHEEL_NEXT[pos] < WHEEL_NEXT[pos-1] {
             return false;
@@ -100,6 +103,7 @@ pub fn is_prime64(target: u64) -> bool {
         return SMALL_PRIMES.binary_search(&(target as u16)).is_ok();
     } else {
         // check remainder against the wheel table
+        // this step eliminates any number that is not coprime to WHEEL_SIZE
         let pos = (target % WHEEL_SIZE as u64) as usize;
         if pos == 0 || WHEEL_NEXT[pos] < WHEEL_NEXT[pos-1] {
             return false;
@@ -158,7 +162,9 @@ pub fn factorize64(target: u64) -> BTreeMap<u64, usize> {
     //      https://github.com/radii/msieve
     //      Pari/GP: ifac_crack
     let mut result = BTreeMap::new();
-    let f2 = target.trailing_zeros(); // quick check on factors of 2
+
+    // quick check on factors of 2
+    let f2 = target.trailing_zeros();
     if f2 == 0 {
         if is_prime64(target) {
             result.insert(target, 1);
@@ -192,34 +198,35 @@ pub fn factorize64(target: u64) -> BTreeMap<u64, usize> {
     }
 
     #[cfg(feature = "big-table")]
-    // divisibility check with pre-computed tables
-    for (&p, (&pinv, plim)) in SMALL_PRIMES
-        .iter()
-        .zip(SMALL_PRIMES_INV.iter().zip(SMALL_PRIMES_INVLIM))
+    // divisibility check with pre-computed tables, see comments on SMALL_PRIMES_INV for reference 
+    for (p, &pinv) in SMALL_PRIMES
+        .iter().map(|&p| p as u64)
+        .zip(SMALL_PRIMES_INV.iter())
         .skip(1)
     {
-        let p64 = p as u64;
-        if p64 > tsqrt {
+        // only need to test primes up to sqrt(target)
+        if p > tsqrt {
             factored = true;
             break;
         }
 
-        let mut r = residual;
-        let mut k: u32 = 0;
+        let mut exp: usize = 0;
         loop {
-            let r2 = r.wrapping_mul(pinv);
-
-            if r2 <= plim {
-                k += 1;
-                r = r2;
-            } else {
-                break;
+            match residual.div_exact(p, &pinv) {
+                Some(q) => {
+                    // residual is divisible by p
+                    exp += 1;
+                    residual = q;
+                },
+                None => {
+                    // otherwise
+                    if exp > 0 {
+                        result.insert(p, exp);
+                    }
+                    break;
+                }
             }
         }
-        if k > 0 {
-            residual = residual / p64.pow(k);
-            result.insert(p64, k as usize);
-        }
         if residual == 1 {
             factored = true;
             break;
@@ -281,6 +288,8 @@ pub fn factorize64(target: u64) -> BTreeMap<u64, usize> {
     result
 }
 
+// TODO: GNU factor uses [Lucas test](https://en.wikipedia.org/wiki/Lucas_primality_test) to prove primality, we could use that as well
+// (only need to test 64bit ~ 128bit)
 pub fn factorize128(target: u128) -> BTreeMap<u128, usize> {
     // shortcut for u64
     if target < (1u128 << 64) {
@@ -291,28 +300,64 @@ pub fn factorize128(target: u128) -> BTreeMap<u128, usize> {
     }
 
     let mut result = BTreeMap::new();
-    let f2 = target.trailing_zeros(); // quick check on factors of 2
+
+    // quick check on factors of 2
+    let f2 = target.trailing_zeros();
     if f2 != 0 {
         result.insert(2, f2 as usize);
     }
+    let mut residual = target >> f2;
 
     // trial division using primes in the table
-    // TODO(v0.3.2): speed up this by precompute tables
-    let mut residual = target >> f2;
+    #[cfg(not(feature = "big-table"))]
     for p in SMALL_PRIMES.iter().skip(1).map(|&v| v as u128) {
         while residual % p == 0 {
             residual = residual / p;
             *result.entry(p).or_insert(0) += 1;
         }
+        if residual == 1 {
+            break;
+        }
     }
+
+    #[cfg(feature = "big-table")]
+    // divisibility check with pre-computed tables, see comments on SMALL_PRIMES_INV for reference 
+    for (p, &pinv) in SMALL_PRIMES
+        .iter().map(|&p| p as u64)
+        .zip(SMALL_PRIMES_INV.iter())
+        .skip(1)
+    {
+        let mut exp: usize = 0;
+        loop {
+            match residual.div_exact(p, &pinv) {
+                Some(q) => {
+                    // residual is divisible by p
+                    exp += 1;
+                    residual = q;
+                },
+                None => {
+                    // otherwise
+                    if exp > 0 {
+                        result.insert(p as u128, exp);
+                    }
+                    break;
+                }
+            }
+        }
+        if residual == 1 {
+            break;
+        }
+    }
+    
     if residual == 1 {
         return result;
     }
 
-    // then try pollard's rho and SQUFOF methods util fully factored
-    let mut todo = vec![residual];
+    // then try pollard's rho util fully factored
+    // TODO: split todo list into large(u128) and small(u64) two lists to utilize the efficient u64 prime test
+    let mut todo = vec![residual]; // cofactors to be processed
     while let Some(target) = todo.pop() {
-        if is_prime(&Mint::from(target), Some(PrimalityTestConfig::bpsw())).probably() {
+        if is_prime(&Mint::from(target), None).probably() {
             *result.entry(target).or_insert(0) += 1;
         } else {
             let divisor = loop {
diff --git a/src/tables.rs b/src/tables.rs
index de9bafb..bc9bdd4 100644
--- a/src/tables.rs
+++ b/src/tables.rs
@@ -88,2066 +88,1040 @@ pub const SMALL_PRIMES: [u16; 1024] = [
 pub const SMALL_PRIMES_NEXT: u64 = 8167;
 
 //////////////////// Pre-computed inversions for primes ////////////////////
+#[cfg(feature = "big-table")]
+type P64 = num_modular::PreInv<u64>;
 
 /// Precomputed modular inverse for fast divisibility check
 ///
-/// We could have store them in u16 and do double width check, but don't bother.
 /// Note that the factor 2 should be eliminated before checking the primes
-/// Reference: <https://math.stackexchange.com/questions/1251327/is-there-a-fast-divisibility-check-for-a-fixed-divisor>
+#[rustfmt::skip]
 #[cfg(feature = "big-table")]
-pub const SMALL_PRIMES_INV: [u64; 1024] = [
-    0x0000000000000000,
-    0xaaaaaaaaaaaaaaab,
-    0xcccccccccccccccd,
-    0x6db6db6db6db6db7,
-    0x2e8ba2e8ba2e8ba3,
-    0x4ec4ec4ec4ec4ec5,
-    0xf0f0f0f0f0f0f0f1,
-    0x86bca1af286bca1b,
-    0xd37a6f4de9bd37a7,
-    0x34f72c234f72c235,
-    0xef7bdef7bdef7bdf,
-    0x14c1bacf914c1bad,
-    0x8f9c18f9c18f9c19,
-    0x82fa0be82fa0be83,
-    0x51b3bea3677d46cf,
-    0x21cfb2b78c13521d,
-    0xcbeea4e1a08ad8f3,
-    0x4fbcda3ac10c9715,
-    0xf0b7672a07a44c6b,
-    0x193d4bb7e327a977,
-    0x7e3f1f8fc7e3f1f9,
-    0x9b8b577e613716af,
-    0xa3784a062b2e43db,
-    0xf47e8fd1fa3f47e9,
-    0xa3a0fd5c5f02a3a1,
-    0x3a4c0a237c32b16d,
-    0xdab7ec1dd3431b57,
-    0x77a04c8f8d28ac43,
-    0xa6c0964fda6c0965,
-    0x90fdbc090fdbc091,
-    0x7efdfbf7efdfbf7f,
-    0x03e88cb3c9484e2b,
-    0xe21a291c077975b9,
-    0x3aef6ca970586723,
-    0xdf5b0f768ce2cabd,
-    0x6fe4dfc9bf937f27,
-    0x5b4fe5e92c0685b5,
-    0x1f693a1c451ab30b,
-    0x8d07aa27db35a717,
-    0x882383b30d516325,
-    0xed6866f8d962ae7b,
-    0x3454dca410f8ed9d,
-    0x1d7ca632ee936f3f,
-    0x70bf015390948f41,
-    0xc96bdb9d3d137e0d,
-    0x2697cc8aef46c0f7,
-    0xc0e8f2a76e68575b,
-    0x687763dfdb43bb1f,
-    0x1b10ea929ba144cb,
-    0x1d10c4c0478bbced,
-    0x63fb9aeb1fdcd759,
-    0x64afaa4f437b2e0f,
-    0xf010fef010fef011,
-    0x28cbfbeb9a020a33,
-    0xff00ff00ff00ff01,
-    0xd624fd1470e99cb7,
-    0x8fb3ddbd6205b5c5,
-    0xd57da36ca27acdef,
-    0xee70c03b25e4463d,
-    0xc5b1a6b80749cb29,
-    0x47768073c9b97113,
-    0x2591e94884ce32ad,
-    0xf02806abc74be1fb,
-    0x7ec3e8f3a7198487,
-    0x58550f8a39409d09,
-    0xec9e48ae6f71de15,
-    0x2ff3a018bfce8063,
-    0x7f9ec3fcf61fe7b1,
-    0x89f5abe570e046d3,
-    0xda971b23f1545af5,
-    0x79d5f00b9a7862a1,
-    0x4dba1df32a128a57,
-    0x87530217b7747d8f,
-    0x30baae53bb5e06dd,
-    0xee70206c12e9b5b3,
-    0xcdde9462ec9dbe7f,
-    0xafb64b05ec41cf4d,
-    0x02944ff5aec02945,
-    0x2cb033128382df71,
-    0x1ccacc0c84b1c2a9,
-    0x19a93db575eb3a0b,
-    0xcebeef94fa86fe2d,
-    0x6faa77fb3f8df54f,
-    0x68a58af00975a751,
-    0xd56e36d0c3efac07,
-    0xd8b44c47a8299b73,
-    0x02d9ccaf9ba70e41,
-    0x0985e1c023d9e879,
-    0x2a343316c494d305,
-    0x70cb7916ab67652f,
-    0xd398f132fb10fe5b,
-    0x6f2a38a6bf54fa1f,
-    0x211df689b98f81d7,
-    0x0e994983e90f1ec3,
-    0xad671e44bed87f3b,
-    0xf9623a0516e70fc7,
-    0x4b7129be9dece355,
-    0x190f3b7473f62c39,
-    0x63dacc9aad46f9a3,
-    0xc1108fda24e8d035,
-    0xb77578472319bd8b,
-    0x473d20a1c7ed9da5,
-    0xfbe85af0fea2c8fb,
-    0x58a1f7e6ce0f4c09,
-    0x1a00e58c544986f3,
-    0x7194a17f55a10dc1,
-    0x7084944785e33763,
-    0xba10679bd84886b1,
-    0xebe9c6bb31260967,
-    0x97a3fe4bd1ff25e9,
-    0x6c6388395b84d99f,
-    0x8c51da6a1335df6d,
-    0x46f3234475d5add9,
-    0x905605ca3c619a43,
-    0xcee8dff304767747,
-    0xff99c27f00663d81,
-    0xacca407f671ddc2b,
-    0xe71298bac1e12337,
-    0xfa1e94309cd09045,
-    0xbebccb8e91496b9b,
-    0x312fa30cc7d7b8bd,
-    0x6160ff9e9f006161,
-    0x6b03673b5e28152d,
-    0xfe802ffa00bfe803,
-    0xe66fe25c9e907c7b,
-    0x3f8b236c76528895,
-    0xf6f923bf01ce2c0d,
-    0x6c3d3d98bed7c42f,
-    0x30981efcd4b010e7,
-    0x6f691fc81ebbe575,
-    0xb10480ddb47b52cb,
-    0x74cd59ed64f3f0d7,
-    0x0105cb81316d6c0f,
-    0x9be64c6d91c1195d,
-    0x71b3f945a27b1f49,
-    0x77d80d50e508fd01,
-    0xa5eb778e133551cd,
-    0x18657d3c2d8a3f1b,
-    0x2e40e220c34ad735,
-    0xa76593c70a714919,
-    0x1eef452124eea383,
-    0x38206dc242ba771d,
-    0x4cd4c35807772287,
-    0x83de917d5e69ddf3,
-    0x882ef0403b4a6c15,
-    0xf8fb6c51c606b677,
-    0xb4abaac446d3e1fd,
-    0xa9f83bbe484a14e9,
-    0x0bebbc0d1ce874d3,
-    0xbd418eaf0473189f,
-    0x44e3af6f372b7e65,
-    0xc87fdace4f9e5d91,
-    0xec93479c446bd9bb,
-    0xdac4d592e777c647,
-    0xa63ea8c8f61f0c23,
-    0xe476062ea5cbbb6f,
-    0xdf68761c69daac27,
-    0xb813d737637aa061,
-    0xa3a77aac1fb15099,
-    0x17f0c3e0712c5825,
-    0xfd912a70ff30637b,
-    0xfbb3b5dc01131289,
-    0x856d560a0f5acdf7,
-    0x96472f314d3f89e3,
-    0xa76f5c7ed2253531,
-    0x816eae7c7bf69fe7,
-    0xb6a2bea4cfb1781f,
-    0xa3900c53318e81ed,
-    0x60aa7f5d9f148d11,
-    0x6be8c0102c7a505d,
-    0x8ff3f0ed28728f33,
-    0x680e0a87e5ec7155,
-    0xbbf70fa49fe829b7,
-    0xd69d1e7b6a50ca39,
-    0x1a1e0f46b6d26aef,
-    0x7429f9a7a8251829,
-    0xd9c2219d1b863613,
-    0x91406c1820d077ad,
-    0x521f4ec02e3d2b97,
-    0xbb8283b63dc8eba5,
-    0x431eda153229ebbf,
-    0xaf0bf78d7e01686b,
-    0xa9ced0742c086e8d,
-    0xc26458ad9f632df9,
-    0xbbff1255dff892af,
-    0xcbd49a333f04d8fd,
-    0xec84ed6f9cfdeff5,
-    0x97980cc40bda9d4b,
-    0x777f34d524f5cbd9,
-    0x2797051d94cbbb7f,
-    0xea769051b4f43b81,
-    0xce7910f3034d4323,
-    0x92791d1374f5b99b,
-    0x89a5645cc68ea1b5,
-    0x5f8aacf796c0cf0b,
-    0xf2e90a15e33edf99,
-    0x8e99e5feb897c451,
-    0xaca2eda38fb91695,
-    0x5d9b737be5ea8b41,
-    0x4aefe1db93fd7cf7,
-    0xa0994ef20b3f8805,
-    0x103890bda912822f,
-    0xb441659d13a9147d,
-    0x1e2134440c4c3f21,
-    0x263a27727a6883c3,
-    0x78e221472ab33855,
-    0x95eac88e82e6faff,
-    0xf66c258317be8dab,
-    0x09ee202c7cb91939,
-    0x8d2fca1042a09ea3,
-    0x82779c856d8b8bf1,
-    0x3879361cba8a223d,
-    0xf23f43639c3182a7,
-    0xa03868fc474bcd13,
-    0x651e78b8c5311a97,
-    0x8ffce639c00c6719,
-    0xf7b460754b0b61cf,
-    0x7b03f3359b8e63b1,
-    0xa55c5326041eb667,
-    0x647f88ab896a76f5,
-    0x8fd971434a55a46d,
-    0x9fbf969958046447,
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-    0x5d7d1b3df70f7ac1,
-    0x16ab7b5e04cc1f6b,
-    0x78a5bfd2e5ececf9,
-    0x6506392e171d869f,
-    0xc3fc12e221ef146d,
-    0xf8aa132822c33657,
-    0x894496574f536f43,
-    0x8b2546b08fb4cbd5,
-    0x043bbb561bd1aa7f,
-    0x2412c7cc4ea7a12b,
-    0x6f0bd406dd71696f,
-    0xad475c6988d54b71,
-    0xd812e5d48dbbba27,
-    0x22aaca437ba04893,
-    0xdba6ff1fecd5f09d,
-    0x13016d3396286773,
-    0xc746494631bcfa41,
-    0xd14888565bf6a10d,
-    0xc002ef885f0adf05,
-    0xe5a04da7fee6ade7,
-    0xc114ce5468593bc7,
-    0x0bb6747dd7f577b7,
-    0x395ce5a20f285839,
-    0x6eee8be66e8618ef,
-    0x52acf64297f1241b,
-    0x361dcc48a364093d,
-    0x342d6f475d72e629,
-    0x5e978bd46410d413,
-    0xcc3433d75ba015ad,
-    0x1c83b7628458d4fb,
-    0xf9ca45637e38f809,
-    0xcbed792ffaf6b115,
-    0x9abd961d8c0e8c8d,
-    0xe69572fa659340af,
-    0x9187e7483a6436fd,
-    0x1e9c726993bed9d9,
-    0x243554db91976365,
-    0x04d06ff994c0088f,
-    0x25b76abcb74889dd,
-    0x3a409642893c779b,
-    0x8f8f620d8bc0c927,
-    0x6f9f196b3369855f,
-    0x92a522bb0638ed99,
-    0x96270f1efdd7004f,
-    0xb4844b380fdaa79d,
-    0x108936aa5f9c1495,
-    0x0b60f606f104c9eb,
-    0xc663dfe8263b302f,
-    0xc91a280b9110b15b,
-    0x0904287118d10969,
-    0x160d36a5d31bf553,
-    0xe84f5fda3c67ad21,
-    0xbd85701f72d4b6ed,
-    0x4c50cf5924dee1c3,
-    0x2455aaf1633bb6e5,
-    0xd775b39f549b8ac7,
-    0x87fcdda7a252cb49,
-    0x53df2e3bd254a739,
-    0x8915e69623a5f7ef,
-    0x1ef24c80742dd08b,
-    0xb4d87aaa6fb1e897,
-    0x788573e8b92dbbfb,
-    0x02527b137b0878c1,
-    0x1870a7c8dee9f4f5,
-    0x39b99e40910a224b,
-    0x45821c0abd4df247,
-    0x10fe2b2f50e02fb3,
-    0x5762b90c043f0345,
-    0x82a67b9193b27bbd,
-    0xa6e914e28ec37693,
-    0x835d9a4facaf445f,
-    0x48def8175884f82d,
-    0xae900e2d7c9a6f7b,
-    0x1c08431bdd18be89,
-    0xb370a66d684fd83f,
-    0xb4be33e18f93b279,
-    0x310c50872a7dd5e3,
-    0x447ab1281276697d,
-    0xc2f122216b2a6c21,
-    0xab99c8b5ae1c3059,
-    0xb78e17a2227d593b,
-    0xabf97d03f7269c5d,
-    0x867aefc9fdbfe7ff,
-    0xf7f7ad182e47d5b7,
-    0x50dff95a9847721b,
-    0xe4cb8a0e83cb6a35,
-    0x8da72ecdf9247a1d,
-    0xc5b04bfc87f31d87,
-    0xe2dcf622ea2b00f3,
-    0xb9ce9f2e4972f46b,
-    0x1ed785c911bf59f9,
-    0x4ddb8a4eed70e085,
-    0x81e93b4df68c24fd,
-    0xee0d0812afcd8357,
-    0xf62e3ba72268a891,
-    0x3194d367c8154147,
-    0xd096ede8e30c20d5,
-    0xd68624d27b87a77f,
-    0xb728fcdc11c8204d,
-    0x9d6b6038077e066f,
-    0xaa732d7a4a360d93,
-    0x36af98a423972db5,
-    0xc31d00da12940f17,
-    0xed85352107410b25,
-    0x829c85ee6db8567b,
-    0xef60258952cc6d89,
-    0xcf28c2e0da787741,
-    0x57567d8494af28f7,
-    0x2c7c98518f174031,
-    0xb28b363a36825ae7,
-    0xed1ffeb64f9ae769,
-    0xcbbb0115e9b9a31f,
-    0x8d3c5fecb7f9e4ed,
-    0x816271698195cfc3,
-    0x9ac939d1c2b1d35d,
-    0xdd9fb7017b0ec455,
-    0xc94cab1e57276e3d,
-    0x8b8806b117c79913,
-    0xa9e63292a3269fd1,
-    0x76da5710f1e989fb,
-    0xdded6688d83a918d,
-    0x4e446b6a305428f9,
-    0x4ddaca7a3696cfb1,
-    0x7eadc4eb87f26ed3,
-    0x76c13a0ff04c00c9,
-    0xcbf800504d2a2681,
-    0x0731dada6c4fec9b,
-    0xbcb52a664e63f627,
-    0xf1f9abda071c2aa9,
-    0xf262ffa620ffe20b,
-    0x93774a3d57199a99,
-    0xfb3541cd467a1903,
-    0x6828cab6b4fe8f51,
-    0x12ac03e3d624cc9d,
-    0x6363bd1e9bb7d7f7,
-    0x334cfd676a484d2f,
-    0xd511acd86f143a53,
-    0x73fc2490e0062be5,
-    0x10780dda36b78b55,
-    0xabf601274064e0ab,
-    0x3ef3e4ca27e4a2cd,
-    0x9216a26e690a16f1,
-    0xbae4849e6034bda7,
-    0xf943a0520e01e9e1,
-    0x7c89958f48f6658b,
-    0xe67128750e0545a5,
-    0xc6c9e1d414516ccf,
-    0x805307f996e9e81d,
-    0x3eddd2cff46ad5bf,
-    0x35582c1aeb5aae85,
-    0x4973c88573ef6eb1,
-    0x3063f627c1e715d9,
-    0x711ad679a8dcc243,
-    0x51c224a17a3db4b3,
-    0x612325ca50ddaed5,
-    0x9929a7b6b7958b37,
-    0xa78d222e5a857bb9,
-    0x3ad0ffe3198d139b,
-    0x08b4659ac547ed17,
-    0x1752e8904aff1003,
-    0x60745c37ee4e5925,
-    0x29e2da1f6557ee51,
-    0x80d78c24ac49cb89,
-    0xc56c3b495c8d1f79,
-    0xcf5bdf9f5088ac2f,
-    0x8a44800e4fae4e7d,
-    0xdd76384277e578e7,
-    0x20b1562d2703facb,
-    0xef56caf96e9d8e3b,
-    0xf54061416aede033,
-    0xe0bc78c21a26e4ff,
-    0x0524f92731a179cd,
-    0x5d3b4ad7deafec8b,
-    0x508828f744da88ad,
-    0x6e82014031710bcf,
-    0xadf3b77a22595dd1,
-    0x0d8f0c03f7ea8a87,
-    0x2c49e3483c3a05f3,
-    0xccecbc98c91274c1,
-    0x273a08941bb71e77,
-    0xdead5a1e3f341baf,
-    0x83eee092593309fd,
-    0x4af5f1bd3ae87ce9,
-    0x4ca85ad2301c9e6d,
-    0x1b19592cd31a3943,
-    0x3e7aa05e6dcd81bb,
-    0x86336cecb02ba47f,
-    0xa96b30d0c8a44b2b,
-    0xb7c63fa0cfca0571,
-    0x8eaf59b405a642b5,
-    0xdf29e9cbb536dc17,
-    0xed14132c82c1d43f,
-    0xaf68778e34caab0d,
-    0xa4f04a3368941d31,
-    0xe9960969357c07e7,
-    0xeb47b62b7360b469,
-    0x64c653d779ae730f,
-    0x479702d3319915c7,
-    0xef3c3eebc6803239,
-    0x93807b1a2e3c0e1b,
-    0x8167e33e3f478029,
-    0x60cb76e38c339397,
-    0xae34788ffe4bc283,
-    0x4b6246a0c6c093a5,
-    0x872e594b12b03efb,
-    0xbc0ae83ce9045b15,
-    0x0ad30a3917e0968d,
-    0x124ef5a4e1c7cd63,
-    0x5b98fe0e9fe17aaf,
-    0x414306cfe45400fd,
-    0xa06d1b4fd391e8bb,
-    0x11939803a60c2381,
-    0x668c11cc37ea6b23,
-    0x83f9b2089dc10645,
-    0x65dc8ae47af277a9,
-    0x6e2368b9c685770b,
-    0x3ea137aeba5a6b2d,
-    0x735f57adca48f19d,
-    0x69a8de0ba1b18107,
-    0x8fb84bdf5822bd79,
-    0xb8fab3b748562721,
-    0xa6c658ea10a65c3b,
-    0xe56381f33ab5e549,
-    0xe3c224da14988139,
-    0x438c253e6d99f513,
-    0xc1b99f8841a3a6e1,
-    0x63fa18c79c54fa8b,
-    0xe7f6f609619d0d1d,
-    0x7b39ef3b70afc109,
-    0x73922c61ca7452bf,
-    0x28d96828332372c1,
-    0x6b6e92968c4e8463,
-    0x571861f084962edb,
-    0xd935c64f140f1ef5,
-    0x96459f8fd72a4c4b,
-    0x410ba9a2a18242d9,
-    0xcf90979f89870391,
-    0x10f94ff26bc00add,
-    0xa6619fbb9da139b3,
-    0x765a23334efb03d5,
-    0x6f2f613b5e631837,
-    0x666b99bfbcd368b9,
-    0x922b78eb01ed45bd,
-    0x7079a199c31de6a9,
-    0xa181abcda167be5f,
-    0x2f6dbbcab3a9822d,
-    0xc5a83ff0e43eba17,
-    0x28c68613dda7d97b,
-    0x5cf33ed49efa5007,
-    0x9125fdead661590d,
-    0xaee67f478c7325e7,
-    0x735b1274a0e89653,
-    0x733b56eae1a4e621,
-    0x1944ffb316ffe65d,
-    0xf26bc3cfd2a01449,
-    0xb5827ba68b83e201,
-    0xac139507e48eefb7,
-    0xeb7676b25834fda3,
-    0xad898f4763da5c1b,
-    0xea906f224398f9a7,
-    0xa8aff3caca28cdad,
-    0x46c53aa36b19b083,
-    0x9ada32b09603e8cf,
-    0xd31f842ef5d8e915,
-    0x6124af44730a33f9,
-    0x828ec4c2b6e64a85,
-    0x3d6f49df999638af,
-    0x7641460a0ea89b65,
-    0x97703f98fb7fe291,
-    0xd343c209e3e6b7b9,
-    0x4e5fc01f6a41406f,
-    0xb78a05b08aa4bcbd,
-    0x3434a14919d34561,
-    0xccead7dee120f525,
-    0xe1375a2bccd87673,
-    0xf727d51420a57141,
-    0x2c3b68cfbcebb00d,
-    0xda91e2f3e17542f7,
-    0xb55f6100ae95d6e3,
-    0x6a0c608e0bbaa975,
-    0xac5f2fc151c016cb,
-    0xb1e5af8146e4d00f,
-    0x6e283d3b112602c7,
-    0xf9a48bcb76c96e55,
-    0xa776780ca4c0e101,
-    0x8d40a2d47d99c7c5,
-    0x4ed9d8a7aedcefef,
-    0x55c5cf9586072313,
-    0x62c640e386ef1f09,
-    0xdb876e7feb8b02f9,
-    0x5b85ac1558bdf263,
-    0xb2b13930c2a889b1,
-    0xdf53c897124f8c57,
-    0x68a69390fdce78dd,
-    0x5a1e8f0261e6e7b3,
-    0xcce38a9ccaab014d,
-    0xb0cd4811fe6a8171,
-    0x911c24573e445027,
-    0x9e86401e61cac4a9,
-    0xfd2731405f265eb5,
-    0x3f4c00205c05b02d,
-    0xe92e3d0a829a974f,
-    0xdec216e5aa47169d,
-    0xa0397bf3448bcd73,
-    0x9ecf538d7efa905b,
-    0xb1037b5f84886421,
-];
-/// Limit of modular inverse muliplied by the target integer. Used together with SMALL_PRIMES_INV
-#[cfg(feature = "big-table")]
-pub const SMALL_PRIMES_INVLIM: [u64; 1024] = [
-    0x7fffffffffffffff,
-    0x5555555555555555,
-    0x3333333333333333,
-    0x2492492492492492,
-    0x1745d1745d1745d1,
-    0x13b13b13b13b13b1,
-    0x0f0f0f0f0f0f0f0f,
-    0x0d79435e50d79435,
-    0x0b21642c8590b216,
-    0x08d3dcb08d3dcb08,
-    0x0842108421084210,
-    0x06eb3e45306eb3e4,
-    0x063e7063e7063e70,
-    0x05f417d05f417d05,
-    0x0572620ae4c415c9,
-    0x04d4873ecade304d,
-    0x0456c797dd49c341,
-    0x04325c53ef368eb0,
-    0x03d226357e16ece5,
-    0x039b0ad12073615a,
-    0x0381c0e070381c0e,
-    0x033d91d2a2067b23,
-    0x03159721ed7e7534,
-    0x02e05c0b81702e05,
-    0x02a3a0fd5c5f02a3,
-    0x0288df0cac5b3f5d,
-    0x027c45979c95204f,
-    0x02647c69456217ec,
-    0x02593f69b02593f6,
-    0x0243f6f0243f6f02,
-    0x0204081020408102,
-    0x01f44659e4a42715,
-    0x01de5d6e3f8868a4,
-    0x01d77b654b82c339,
-    0x01b7d6c3dda338b2,
-    0x01b2036406c80d90,
-    0x01a16d3f97a4b01a,
-    0x01920fb49d0e228d,
-    0x01886e5f0abb0499,
-    0x017ad2208e0ecc35,
-    0x016e1f76b4337c6c,
-    0x016a13cd15372904,
-    0x01571ed3c506b39a,
-    0x015390948f40feac,
-    0x014cab88725af6e7,
-    0x0149539e3b2d066e,
-    0x013698df3de07479,
-    0x0125e22708092f11,
-    0x0120b470c67c0d88,
-    0x011e2ef3b3fb8744,
-    0x0119453808ca29c0,
-    0x0112358e75d30336,
-    0x010fef010fef010f,
-    0x0105197f7d734041,
-    0x00ff00ff00ff00ff,
-    0x00f92fb2211855a8,
-    0x00f3a0d52cba8723,
-    0x00f1d48bcee0d399,
-    0x00ec979118f3fc4d,
-    0x00e939651fe2d8d3,
-    0x00e79372e225fe30,
-    0x00dfac1f74346c57,
-    0x00d578e97c3f5fe5,
-    0x00d2ba083b445250,
-    0x00d161543e28e502,
-    0x00cebcf8bb5b4169,
-    0x00c5fe740317f9d0,
-    0x00c2780613c0309e,
-    0x00bcdd535db1cc5b,
-    0x00bbc8408cd63069,
-    0x00b9a7862a0ff465,
-    0x00b68d31340e4307,
-    0x00b2927c29da5519,
-    0x00afb321a1496fdf,
-    0x00aceb0f891e6551,
-    0x00ab1cbdd3e2970f,
-    0x00a87917088e262b,
-    0x00a513fd6bb00a51,
-    0x00a36e71a2cb0331,
-    0x00a03c1688732b30,
-    0x009c69169b30446d,
-    0x009baade8e4a2f6e,
-    0x00980e4156201301,
-    0x00975a750ff68a58,
-    0x009548e4979e0829,
-    0x0093efd1c50e726b,
-    0x0091f5bcb8bb02d9,
-    0x008f67a1e3fdc261,
-    0x008e2917e0e702c6,
-    0x008d8be33f95d715,
-    0x008c55841c815ed5,
-    0x0088d180cd3a4133,
-    0x00869222b1acf1ce,
-    0x0085797b917765ab,
-    0x008355ace3c897db,
-    0x00824a4e60b3262b,
-    0x0080c121b28bd1ba,
-    0x007dc9f3397d4c29,
-    0x007d4ece8fe88139,
-    0x0079237d65bcce50,
-    0x0077cf53c5f7936c,
-    0x0075a8accfbdd11e,
-    0x007467ac557c228e,
-    0x00732d70ed8db8e9,
-    0x0072c62a24c3797f,
-    0x007194a17f55a10d,
-    0x006fa549b41da7e7,
-    0x006e8419e6f61221,
-    0x006d68b5356c207b,
-    0x006d0b803685c01b,
-    0x006bf790a8b2d207,
-    0x006ae907ef4b96c2,
-    0x006a37991a23aead,
-    0x0069dfbdd4295b66,
-    0x0067dc4c45c8033e,
-    0x00663d80ff99c27f,
-    0x0065ec17e3559948,
-    0x00654ac835cfba5c,
-    0x00645c854ae10772,
-    0x006372990e5f901f,
-    0x006325913c07beef,
-    0x006160ff9e9f0061,
-    0x0060cdb520e5e88e,
-    0x005ff4017fd005ff,
-    0x005ed79e31a4dccd,
-    0x005d7d42d48ac5ef,
-    0x005c6f35ccba5028,
-    0x005b2618ec6ad0a5,
-    0x005a2553748e42e7,
-    0x0059686cf744cd5b,
-    0x0058ae97bab79976,
-    0x0058345f1876865f,
-    0x005743d5bb24795a,
-    0x005692c4d1ab74ab,
-    0x00561e46a4d5f337,
-    0x005538ed06533997,
-    0x0054c807f2c0bec2,
-    0x005345efbc572d36,
-    0x00523a758f941345,
-    0x005102370f816c89,
-    0x0050cf129fb94acf,
-    0x004fd31941cafdd1,
-    0x004fa1704aa75945,
-    0x004f3ed6d45a63ad,
-    0x004f0de57154ebed,
-    0x004e1cae8815f811,
-    0x004cd47ba5f6ff19,
-    0x004c78ae734df709,
-    0x004c4b19ed85cfb8,
-    0x004bf093221d1218,
-    0x004aba3c21dc633f,
-    0x004a6360c344de00,
-    0x004a383e9f74d68a,
-    0x0049e28fbabb9940,
-    0x0048417b57c78cd7,
-    0x0047f043713f3a2b,
-    0x00474ff2a10281cf,
-    0x00468b6f9a978f91,
-    0x0045f13f1caff2e2,
-    0x0045a5228cec23e9,
-    0x0045342c556c66b9,
-    0x0044c4a23feeced7,
-    0x0043c5c20d3c9fe6,
-    0x00437e494b239798,
-    0x0043142d118e47cb,
-    0x0042ab5c73a13458,
-    0x004221950db0f3db,
-    0x0041bbb2f80a4553,
-    0x0040f391612c6680,
-    0x0040b1e94173fefd,
-    0x004050647d9d0445,
-    0x004030241b144f3b,
-    0x003f90c2ab542cb1,
-    0x003f71412d59f597,
-    0x003f137701b98841,
-    0x003e79886b60e278,
-    0x003e5b1916a7181d,
-    0x003dc4a50968f524,
-    0x003da6e4c9550321,
-    0x003d4e4f06f1def3,
-    0x003c4a6bdd24f9a4,
-    0x003c11d54b525c73,
-    0x003bf5b1c5721065,
-    0x003bbdb9862f23b4,
-    0x003b6a8801db5440,
-    0x003b183cf0fed886,
-    0x003aabe394bdc3f4,
-    0x003a5ba3e76156da,
-    0x003a0c3e953378db,
-    0x0038f03561320b1e,
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-    0x000c3f57990b87a1,
-    0x000c2ddcb31250f8,
-    0x000c2a63b3651432,
-    0x000c26ecae1db72e,
-    0x000c2377a18c051e,
-    0x000c1ede9efcec29,
-    0x000c1b6e258d13a0,
-    0x000c19243f5399bb,
-    0x000c17ff9f400305,
-    0x000c112865703b94,
-    0x000c0dbfaea33225,
-    0x000c0b7af12ddfb9,
-    0x000c0a58e464462c,
-    0x000c06f40512eef2,
-    0x000bfa9275a2b247,
-    0x000bf7367402cdf0,
-    0x000bf61833f4f921,
-    0x000bf3dc543a74a1,
-    0x000be9d9302a7115,
-    0x000be8bd6e051e01,
-    0x000be6868804d5a6,
-    0x000bdfe6c4359f0e,
-    0x000bdeccdb0b5c3a,
-    0x000bdb8058ee429a,
-    0x000bd94e5c1b371f,
-    0x000bcb1d293b1af3,
-    0x000bc7db8db0c1a5,
-    0x000bc49bbdfd2662,
-    0x000bc2723240f402,
-    0x000bbe217c2b7c13,
-    0x000bb8c10aab27b2,
-    0x000ba7ad528a7e79,
-    0x000b9f3611b48c5e,
-    0x000b9e2806e5e7c4,
-    0x000b9aff0c4913fe,
-    0x000b98e4aedd581c,
-    0x000b97d7c94b7dc2,
-    0x000b95be902d9d9e,
-    0x000b94b23c872b90,
-    0x000b8f77714d15a1,
-    0x000b882d0beff6a1,
-    0x000b850ff9852703,
-    0x000b82fd86db8806,
-    0x000b7edadd32f76c,
-    0x000b79b3b4df3b7b,
-    0x000b769e6d59833f,
-    0x000b6c636b5141ff,
-    0x000b6a59ceae8801,
-    0x000b6955461e38f7,
-    0x000b6648c2dc6bc2,
-    0x000b572282260209,
-    0x000b552072bde889,
-    0x000b511e7552f9c4,
-    0x000b4c1ff34a5c0e,
-    0x000b4922f58d4aa2,
-    0x000b46278c16b967,
-    0x000b42301cd99b49,
-    0x000b3f385dd77e4e,
-    0x000b394d8ef8f0f6,
-    0x000b375601507c14,
-    0x000b3463f76be376,
-    0x000b3368f6c4a07c,
-    0x000b3078fc1c25f0,
-    0x000b2e84854e93e5,
-    0x000b2b971aa909a4,
-    0x000b2a9da39d6bc8,
-    0x000b25c0dc29a0fc,
-    0x000b24c8698449a7,
-    0x000b1d0ae579aefe,
-    0x000b1a2698ea2f9e,
-    0x000b108dc4186078,
-    0x000b0ea463b00212,
-    0x000b08ec37007962,
-    0x000b024778cc023c,
-    0x000af515df36a88e,
-    0x000af24635f6561e,
-    0x000ae8f1b92baeaf,
-    0x000ae715eee11f8e,
-    0x000adec0b0a3bb36,
-    0x000adb10aa4c956f,
-    0x000ad84e49752245,
-    0x000ad6782597f0c2,
-    0x000ad3b81a0d72fe,
-    0x000acd52beced79e,
-    0x000aca9755063254,
-    0x000ac7dd4cafb12a,
-    0x000ac354f80dca44,
-    0x000ac26d5c2b8ad2,
-    0x000abde997dabd3d,
-    0x000ab883aa1100a0,
-    0x000ab4ed637f5a0b,
-    0x000ab074e9febf52,
-    0x000aaf90778c2039,
-    0x000aab1c7684f034,
-    0x000aa78f20ebbb3e,
-    0x000aa23f8dafd4cc,
-    0x000a9dd69cad5934,
-    0x000a935004a07302,
-    0x000a9270690f3d14,
-    0x000a90b1a0aa5d30,
-    0x000a8d35c9d731e9,
-    0x000a8a9a6a51f16c,
-    0x000a88de370f596b,
-    0x000a856786adae36,
-    0x000a7da4c77d3161,
-    0x000a7959f863d4a1,
-    0x000a76c85e80c195,
-    0x000a743806dc44c4,
-    0x000a735d866dfa0a,
-    0x000a70cedb02531e,
-    0x000a6c8e842c770f,
-    0x000a67791215dd74,
-    0x000a66a0a51d363d,
-    0x000a626893011861,
-    0x000a5fe22c55c089,
-    0x000a5d5cffb77275,
-    0x000a5ad90c4186e5,
-    0x000a578057e7c2eb,
-    0x000a54ff3bb10e91,
-    0x000a50d5683edc94,
-    0x000a4e57854b3df4,
-    0x000a4d8328c4b800,
-    0x000a4b06e01d97b3,
-    0x000a488bca2c4449,
-    0x000a4611e6132ed5,
-    0x000a41f40f39e646,
-    0x000a3eab5c3e44e9,
-    0x000a34ddd50561e0,
-    0x000a326d60e94186,
-    0x000a2985a81ce614,
-    0x000a28b72e26f82e,
-    0x000a217aa3479693,
-    0x000a1fe05c62df4b,
-    0x000a1cad538aebf9,
-    0x000a18b05f490083,
-    0x000a0ccc4c28fc31,
-    0x000a09a544d01ffe,
-    0x000a0294aa53e9a2,
-    0x000a01041a6aaed5,
-    0x000a003c01680870,
-    0x0009fc5558a971c8,
-    0x0009f9ff9c3c03e5,
-    0x0009f9389b864ab9,
-    0x0009f6e4534bdca8,
-    0x0009f557687235c2,
-    0x0009ee633c0391ab,
-    0x0009eb4f28e0bb39,
-    0x0009e6b49e92e4bb,
-    0x0009dfd4ccbd0045,
-    0x0009d9c0828536c1,
-    0x0009d77ad449f777,
-    0x0009d6b92b28ee48,
-    0x0009d231a476ed51,
-    0x0009cfef711bf120,
-    0x0009cc2e1448b765,
-    0x0009cb6e26cbc64d,
-    0x0009c7b03b4a9c67,
-    0x0009c6f0fd980ab1,
-    0x0009c4b3f3a30c3f,
-    0x0009c0fb29436687,
-    0x0009bbca025b7aec,
-    0x0009ba4f4421e52c,
-    0x0009b1783809ff03,
-    0x0009b0bc5b4d2eac,
-    0x0009aae172fd8b9c,
-    0x0009aa26954607ed,
-    0x0009a681e758a022,
-    0x0009a5c7b284942e,
-    0x0009a2264ecc5558,
-    0x00099aebb39be56f,
-    0x0009997ae1a9faac,
-    0x000998c2a22b6900,
-    0x000997527603f8a8,
-    0x00099473685e4d50,
-    0x00098eba72512a13,
-    0x00098c96d8dee9e1,
-    0x00098a743453554e,
-    0x000989be33c9e6bd,
-    0x0009857c692e9a59,
-    0x00097fd540c05c9e,
-    0x00097d04302ed944,
-    0x00097b9c48289935,
-    0x0009798133ece717,
-    0x00096f07c683689e,
-    0x00096e55d6393fc5,
-    0x00096addad861696,
-    0x00096a2c5a2cf0cf,
-    0x00096818fc825eba,
-    0x000966b74027f48a,
-    0x000964a56850b8ed,
-    0x000962947990eb36,
-    0x00095fd4a4c885e0,
-    0x00095dc5d3954fde,
-    0x00095c671ddfe516,
-    0x0009584d6340ddf1,
-    0x00095641de84afcc,
-    0x000953893c386521,
-    0x00094f7740d87794,
-    0x00094e1cb70c9ce0,
-    0x00094962ecbcc7ce,
-    0x00094559c69059cf,
-    0x000941ff7e640716,
-    0x000939fd7a24b099,
-    0x000937ff22c014bd,
-    0x000934050872c09e,
-    0x00093209446d56f6,
-    0x0009316033b5bd22,
-    0x00092a22b9a79374,
-    0x000927838edba206,
-    0x000921a2e7112833,
-    0x00091e623d5660d0,
-    0x00091c6fc0cab8b6,
-    0x000917e7d88028eb,
-    0x0009169d455585cd,
-    0x000915f81ef2d529,
-    0x0009140938595d3a,
-    0x000910d2360a450e,
-    0x00090e417104eabd,
-    0x00090c55d0fdea28,
-    0x00090b0e84c04f20,
-    0x000909243fac6b70,
-    0x0008ff9d0440d137,
-    0x0008fb3192789d73,
-    0x0008f80c0d5031e3,
-    0x0008f76b3664f164,
-    0x0008f3a80550abc3,
-    0x0008f087c50e00c4,
-    0x0008efe7fb408cc2,
-    0x0008eaecce5c4fd7,
-    0x0008ea4dccaaec0b,
-    0x0008e4ba9fbc2ff0,
-    0x0008dd5688a3b7d6,
-    0x0008d7d3821fd94f,
-    0x0008d5feb03c31d7,
-    0x0008d12033cc9d30,
-    0x0008cbac4dec6a82,
-    0x0008c9dc80ab604b,
-    0x0008c942115dcc96,
-    0x0008c3d7df67b539,
-    0x0008c2a4bc35cb3b,
-    0x0008c0d8a4f1f264,
-    0x0008c03f71cbf906,
-    0x0008bd42abd9a107,
-    0x0008bae051d7f6ff,
-    0x0008b7e735068135,
-    0x0008b61f82c5fb08,
-    0x0008b4588a74a05a,
-    0x0008b1fb0a7ed403,
-    0x0008b0ccc5d8f5c8,
-    0x0008af07f8ac5146,
-    0x0008ae71328ffd49,
-    0x0008ab8086624822,
-    0x0008aaea3ab5ae89,
-    0x0008a7661f7020fe,
-    0x0008a63ab88aa8dd,
-    0x0008a47a35d020f3,
-    0x0008a2ba68a3cebf,
-    0x0008a2254c852497,
-    0x00089ea849898bb3,
-    0x00089d7f3e285109,
-    0x000899720af36739,
-    0x00089442160d11dc,
-    0x0008931bd5875a22,
-    0x000891630877aedf,
-    0x00088baaad83e38f,
-    0x00088a86b9090aa4,
-    0x0008883fb99bf244,
-    0x0008868b45e727ee,
-    0x00088568aef30d47,
-    0x0008832468f0bcdd,
-    0x00088202b9a4df76,
-    0x00087e0f31872e9b,
-    0x00087c5ecd731f42,
-    0x00087b3eea3bb388,
-    0x00087751a6c67d78,
-    0x000873f6e2f9d34a,
-    0x000872d938dcfc01,
-    0x0008724a80151dba,
-    0x000869f677f6cc1a,
-    0x000868db701df58d,
-    0x0008623f563a7d6d,
-    0x00086099ef0c8886,
-    0x00085ef52d38fe87,
-    0x00085bad981c7847,
-    0x0008586893de7cfc,
-    0x0008549b491e9efe,
-    0x000852fb3859bea4,
-    0x000851e631fc08f8,
-    0x0008515bc9cde5f1,
-    0x000850472f6185b3,
-    0x00084b6defbc166b,
-    0x000849d17159854b,
-    0x0008469a54a20645,
-    0x00084476f9401ade,
-    0x000842dd2e2dc25d,
-    0x000841cc543f58cb,
-    0x00083e9b6c3df688,
-    0x00083e1382f22ff9,
-    0x00083ae57a327933,
-    0x000832fd15e00939,
-    0x00082ecb9c6669ac,
-    0x00082e45ba6652c4,
-    0x00082cb47b00abaa,
-    0x000826fa5d0ce5aa,
-    0x000823598cfc6865,
-    0x000821cc79da73f1,
-    0x00081f37ff3d12c0,
-    0x00081c21947b0acd,
-    0x00081a97404af5f7,
-    0x00081a13f02d110e,
-    0x0008190d81c9877b,
-    0x000817016c0b3ffd,
-    0x00081473c50ac33e,
-    0x000812ec59f2d11a,
-    0x0008116582e237c8,
-    0x00080b4fe85ec545,
-    0x000807c7894d029a,
+pub const SMALL_PRIMES_INV: [P64; 1024] = [
+    // the first should be 2, but 2 has not modular inverse
+    P64::new(0x0000000000000001, 0xffffffffffffffff),
+    P64::new(0xaaaaaaaaaaaaaaab, 0x5555555555555555),
+    P64::new(0xcccccccccccccccd, 0x3333333333333333),
+    P64::new(0x6db6db6db6db6db7, 0x2492492492492492),
+    P64::new(0x2e8ba2e8ba2e8ba3, 0x1745d1745d1745d1),
+    P64::new(0x4ec4ec4ec4ec4ec5, 0x13b13b13b13b13b1),
+    P64::new(0xf0f0f0f0f0f0f0f1, 0x0f0f0f0f0f0f0f0f),
+    P64::new(0x86bca1af286bca1b, 0x0d79435e50d79435),
+    P64::new(0xd37a6f4de9bd37a7, 0x0b21642c8590b216),
+    P64::new(0x34f72c234f72c235, 0x08d3dcb08d3dcb08),
+    P64::new(0xef7bdef7bdef7bdf, 0x0842108421084210),
+    P64::new(0x14c1bacf914c1bad, 0x06eb3e45306eb3e4),
+    P64::new(0x8f9c18f9c18f9c19, 0x063e7063e7063e70),
+    P64::new(0x82fa0be82fa0be83, 0x05f417d05f417d05),
+    P64::new(0x51b3bea3677d46cf, 0x0572620ae4c415c9),
+    P64::new(0x21cfb2b78c13521d, 0x04d4873ecade304d),
+    P64::new(0xcbeea4e1a08ad8f3, 0x0456c797dd49c341),
+    P64::new(0x4fbcda3ac10c9715, 0x04325c53ef368eb0),
+    P64::new(0xf0b7672a07a44c6b, 0x03d226357e16ece5),
+    P64::new(0x193d4bb7e327a977, 0x039b0ad12073615a),
+    P64::new(0x7e3f1f8fc7e3f1f9, 0x0381c0e070381c0e),
+    P64::new(0x9b8b577e613716af, 0x033d91d2a2067b23),
+    P64::new(0xa3784a062b2e43db, 0x03159721ed7e7534),
+    P64::new(0xf47e8fd1fa3f47e9, 0x02e05c0b81702e05),
+    P64::new(0xa3a0fd5c5f02a3a1, 0x02a3a0fd5c5f02a3),
+    P64::new(0x3a4c0a237c32b16d, 0x0288df0cac5b3f5d),
+    P64::new(0xdab7ec1dd3431b57, 0x027c45979c95204f),
+    P64::new(0x77a04c8f8d28ac43, 0x02647c69456217ec),
+    P64::new(0xa6c0964fda6c0965, 0x02593f69b02593f6),
+    P64::new(0x90fdbc090fdbc091, 0x0243f6f0243f6f02),
+    P64::new(0x7efdfbf7efdfbf7f, 0x0204081020408102),
+    P64::new(0x03e88cb3c9484e2b, 0x01f44659e4a42715),
+    P64::new(0xe21a291c077975b9, 0x01de5d6e3f8868a4),
+    P64::new(0x3aef6ca970586723, 0x01d77b654b82c339),
+    P64::new(0xdf5b0f768ce2cabd, 0x01b7d6c3dda338b2),
+    P64::new(0x6fe4dfc9bf937f27, 0x01b2036406c80d90),
+    P64::new(0x5b4fe5e92c0685b5, 0x01a16d3f97a4b01a),
+    P64::new(0x1f693a1c451ab30b, 0x01920fb49d0e228d),
+    P64::new(0x8d07aa27db35a717, 0x01886e5f0abb0499),
+    P64::new(0x882383b30d516325, 0x017ad2208e0ecc35),
+    P64::new(0xed6866f8d962ae7b, 0x016e1f76b4337c6c),
+    P64::new(0x3454dca410f8ed9d, 0x016a13cd15372904),
+    P64::new(0x1d7ca632ee936f3f, 0x01571ed3c506b39a),
+    P64::new(0x70bf015390948f41, 0x015390948f40feac),
+    P64::new(0xc96bdb9d3d137e0d, 0x014cab88725af6e7),
+    P64::new(0x2697cc8aef46c0f7, 0x0149539e3b2d066e),
+    P64::new(0xc0e8f2a76e68575b, 0x013698df3de07479),
+    P64::new(0x687763dfdb43bb1f, 0x0125e22708092f11),
+    P64::new(0x1b10ea929ba144cb, 0x0120b470c67c0d88),
+    P64::new(0x1d10c4c0478bbced, 0x011e2ef3b3fb8744),
+    P64::new(0x63fb9aeb1fdcd759, 0x0119453808ca29c0),
+    P64::new(0x64afaa4f437b2e0f, 0x0112358e75d30336),
+    P64::new(0xf010fef010fef011, 0x010fef010fef010f),
+    P64::new(0x28cbfbeb9a020a33, 0x0105197f7d734041),
+    P64::new(0xff00ff00ff00ff01, 0x00ff00ff00ff00ff),
+    P64::new(0xd624fd1470e99cb7, 0x00f92fb2211855a8),
+    P64::new(0x8fb3ddbd6205b5c5, 0x00f3a0d52cba8723),
+    P64::new(0xd57da36ca27acdef, 0x00f1d48bcee0d399),
+    P64::new(0xee70c03b25e4463d, 0x00ec979118f3fc4d),
+    P64::new(0xc5b1a6b80749cb29, 0x00e939651fe2d8d3),
+    P64::new(0x47768073c9b97113, 0x00e79372e225fe30),
+    P64::new(0x2591e94884ce32ad, 0x00dfac1f74346c57),
+    P64::new(0xf02806abc74be1fb, 0x00d578e97c3f5fe5),
+    P64::new(0x7ec3e8f3a7198487, 0x00d2ba083b445250),
+    P64::new(0x58550f8a39409d09, 0x00d161543e28e502),
+    P64::new(0xec9e48ae6f71de15, 0x00cebcf8bb5b4169),
+    P64::new(0x2ff3a018bfce8063, 0x00c5fe740317f9d0),
+    P64::new(0x7f9ec3fcf61fe7b1, 0x00c2780613c0309e),
+    P64::new(0x89f5abe570e046d3, 0x00bcdd535db1cc5b),
+    P64::new(0xda971b23f1545af5, 0x00bbc8408cd63069),
+    P64::new(0x79d5f00b9a7862a1, 0x00b9a7862a0ff465),
+    P64::new(0x4dba1df32a128a57, 0x00b68d31340e4307),
+    P64::new(0x87530217b7747d8f, 0x00b2927c29da5519),
+    P64::new(0x30baae53bb5e06dd, 0x00afb321a1496fdf),
+    P64::new(0xee70206c12e9b5b3, 0x00aceb0f891e6551),
+    P64::new(0xcdde9462ec9dbe7f, 0x00ab1cbdd3e2970f),
+    P64::new(0xafb64b05ec41cf4d, 0x00a87917088e262b),
+    P64::new(0x02944ff5aec02945, 0x00a513fd6bb00a51),
+    P64::new(0x2cb033128382df71, 0x00a36e71a2cb0331),
+    P64::new(0x1ccacc0c84b1c2a9, 0x00a03c1688732b30),
+    P64::new(0x19a93db575eb3a0b, 0x009c69169b30446d),
+    P64::new(0xcebeef94fa86fe2d, 0x009baade8e4a2f6e),
+    P64::new(0x6faa77fb3f8df54f, 0x00980e4156201301),
+    P64::new(0x68a58af00975a751, 0x00975a750ff68a58),
+    P64::new(0xd56e36d0c3efac07, 0x009548e4979e0829),
+    P64::new(0xd8b44c47a8299b73, 0x0093efd1c50e726b),
+    P64::new(0x02d9ccaf9ba70e41, 0x0091f5bcb8bb02d9),
+    P64::new(0x0985e1c023d9e879, 0x008f67a1e3fdc261),
+    P64::new(0x2a343316c494d305, 0x008e2917e0e702c6),
+    P64::new(0x70cb7916ab67652f, 0x008d8be33f95d715),
+    P64::new(0xd398f132fb10fe5b, 0x008c55841c815ed5),
+    P64::new(0x6f2a38a6bf54fa1f, 0x0088d180cd3a4133),
+    P64::new(0x211df689b98f81d7, 0x00869222b1acf1ce),
+    P64::new(0x0e994983e90f1ec3, 0x0085797b917765ab),
+    P64::new(0xad671e44bed87f3b, 0x008355ace3c897db),
+    P64::new(0xf9623a0516e70fc7, 0x00824a4e60b3262b),
+    P64::new(0x4b7129be9dece355, 0x0080c121b28bd1ba),
+    P64::new(0x190f3b7473f62c39, 0x007dc9f3397d4c29),
+    P64::new(0x63dacc9aad46f9a3, 0x007d4ece8fe88139),
+    P64::new(0xc1108fda24e8d035, 0x0079237d65bcce50),
+    P64::new(0xb77578472319bd8b, 0x0077cf53c5f7936c),
+    P64::new(0x473d20a1c7ed9da5, 0x0075a8accfbdd11e),
+    P64::new(0xfbe85af0fea2c8fb, 0x007467ac557c228e),
+    P64::new(0x58a1f7e6ce0f4c09, 0x00732d70ed8db8e9),
+    P64::new(0x1a00e58c544986f3, 0x0072c62a24c3797f),
+    P64::new(0x7194a17f55a10dc1, 0x007194a17f55a10d),
+    P64::new(0x7084944785e33763, 0x006fa549b41da7e7),
+    P64::new(0xba10679bd84886b1, 0x006e8419e6f61221),
+    P64::new(0xebe9c6bb31260967, 0x006d68b5356c207b),
+    P64::new(0x97a3fe4bd1ff25e9, 0x006d0b803685c01b),
+    P64::new(0x6c6388395b84d99f, 0x006bf790a8b2d207),
+    P64::new(0x8c51da6a1335df6d, 0x006ae907ef4b96c2),
+    P64::new(0x46f3234475d5add9, 0x006a37991a23aead),
+    P64::new(0x905605ca3c619a43, 0x0069dfbdd4295b66),
+    P64::new(0xcee8dff304767747, 0x0067dc4c45c8033e),
+    P64::new(0xff99c27f00663d81, 0x00663d80ff99c27f),
+    P64::new(0xacca407f671ddc2b, 0x0065ec17e3559948),
+    P64::new(0xe71298bac1e12337, 0x00654ac835cfba5c),
+    P64::new(0xfa1e94309cd09045, 0x00645c854ae10772),
+    P64::new(0xbebccb8e91496b9b, 0x006372990e5f901f),
+    P64::new(0x312fa30cc7d7b8bd, 0x006325913c07beef),
+    P64::new(0x6160ff9e9f006161, 0x006160ff9e9f0061),
+    P64::new(0x6b03673b5e28152d, 0x0060cdb520e5e88e),
+    P64::new(0xfe802ffa00bfe803, 0x005ff4017fd005ff),
+    P64::new(0xe66fe25c9e907c7b, 0x005ed79e31a4dccd),
+    P64::new(0x3f8b236c76528895, 0x005d7d42d48ac5ef),
+    P64::new(0xf6f923bf01ce2c0d, 0x005c6f35ccba5028),
+    P64::new(0x6c3d3d98bed7c42f, 0x005b2618ec6ad0a5),
+    P64::new(0x30981efcd4b010e7, 0x005a2553748e42e7),
+    P64::new(0x6f691fc81ebbe575, 0x0059686cf744cd5b),
+    P64::new(0xb10480ddb47b52cb, 0x0058ae97bab79976),
+    P64::new(0x74cd59ed64f3f0d7, 0x0058345f1876865f),
+    P64::new(0x0105cb81316d6c0f, 0x005743d5bb24795a),
+    P64::new(0x9be64c6d91c1195d, 0x005692c4d1ab74ab),
+    P64::new(0x71b3f945a27b1f49, 0x00561e46a4d5f337),
+    P64::new(0x77d80d50e508fd01, 0x005538ed06533997),
+    P64::new(0xa5eb778e133551cd, 0x0054c807f2c0bec2),
+    P64::new(0x18657d3c2d8a3f1b, 0x005345efbc572d36),
+    P64::new(0x2e40e220c34ad735, 0x00523a758f941345),
+    P64::new(0xa76593c70a714919, 0x005102370f816c89),
+    P64::new(0x1eef452124eea383, 0x0050cf129fb94acf),
+    P64::new(0x38206dc242ba771d, 0x004fd31941cafdd1),
+    P64::new(0x4cd4c35807772287, 0x004fa1704aa75945),
+    P64::new(0x83de917d5e69ddf3, 0x004f3ed6d45a63ad),
+    P64::new(0x882ef0403b4a6c15, 0x004f0de57154ebed),
+    P64::new(0xf8fb6c51c606b677, 0x004e1cae8815f811),
+    P64::new(0xb4abaac446d3e1fd, 0x004cd47ba5f6ff19),
+    P64::new(0xa9f83bbe484a14e9, 0x004c78ae734df709),
+    P64::new(0x0bebbc0d1ce874d3, 0x004c4b19ed85cfb8),
+    P64::new(0xbd418eaf0473189f, 0x004bf093221d1218),
+    P64::new(0x44e3af6f372b7e65, 0x004aba3c21dc633f),
+    P64::new(0xc87fdace4f9e5d91, 0x004a6360c344de00),
+    P64::new(0xec93479c446bd9bb, 0x004a383e9f74d68a),
+    P64::new(0xdac4d592e777c647, 0x0049e28fbabb9940),
+    P64::new(0xa63ea8c8f61f0c23, 0x0048417b57c78cd7),
+    P64::new(0xe476062ea5cbbb6f, 0x0047f043713f3a2b),
+    P64::new(0xdf68761c69daac27, 0x00474ff2a10281cf),
+    P64::new(0xb813d737637aa061, 0x00468b6f9a978f91),
+    P64::new(0xa3a77aac1fb15099, 0x0045f13f1caff2e2),
+    P64::new(0x17f0c3e0712c5825, 0x0045a5228cec23e9),
+    P64::new(0xfd912a70ff30637b, 0x0045342c556c66b9),
+    P64::new(0xfbb3b5dc01131289, 0x0044c4a23feeced7),
+    P64::new(0x856d560a0f5acdf7, 0x0043c5c20d3c9fe6),
+    P64::new(0x96472f314d3f89e3, 0x00437e494b239798),
+    P64::new(0xa76f5c7ed2253531, 0x0043142d118e47cb),
+    P64::new(0x816eae7c7bf69fe7, 0x0042ab5c73a13458),
+    P64::new(0xb6a2bea4cfb1781f, 0x004221950db0f3db),
+    P64::new(0xa3900c53318e81ed, 0x0041bbb2f80a4553),
+    P64::new(0x60aa7f5d9f148d11, 0x0040f391612c6680),
+    P64::new(0x6be8c0102c7a505d, 0x0040b1e94173fefd),
+    P64::new(0x8ff3f0ed28728f33, 0x004050647d9d0445),
+    P64::new(0x680e0a87e5ec7155, 0x004030241b144f3b),
+    P64::new(0xbbf70fa49fe829b7, 0x003f90c2ab542cb1),
+    P64::new(0xd69d1e7b6a50ca39, 0x003f71412d59f597),
+    P64::new(0x1a1e0f46b6d26aef, 0x003f137701b98841),
+    P64::new(0x7429f9a7a8251829, 0x003e79886b60e278),
+    P64::new(0xd9c2219d1b863613, 0x003e5b1916a7181d),
+    P64::new(0x91406c1820d077ad, 0x003dc4a50968f524),
+    P64::new(0x521f4ec02e3d2b97, 0x003da6e4c9550321),
+    P64::new(0xbb8283b63dc8eba5, 0x003d4e4f06f1def3),
+    P64::new(0x431eda153229ebbf, 0x003c4a6bdd24f9a4),
+    P64::new(0xaf0bf78d7e01686b, 0x003c11d54b525c73),
+    P64::new(0xa9ced0742c086e8d, 0x003bf5b1c5721065),
+    P64::new(0xc26458ad9f632df9, 0x003bbdb9862f23b4),
+    P64::new(0xbbff1255dff892af, 0x003b6a8801db5440),
+    P64::new(0xcbd49a333f04d8fd, 0x003b183cf0fed886),
+    P64::new(0xec84ed6f9cfdeff5, 0x003aabe394bdc3f4),
+    P64::new(0x97980cc40bda9d4b, 0x003a5ba3e76156da),
+    P64::new(0x777f34d524f5cbd9, 0x003a0c3e953378db),
+    P64::new(0x2797051d94cbbb7f, 0x0038f03561320b1e),
+    P64::new(0xea769051b4f43b81, 0x0038d6ecaef5908a),
+    P64::new(0xce7910f3034d4323, 0x003859cf221e6069),
+    P64::new(0x92791d1374f5b99b, 0x0037f7415dc9588a),
+    P64::new(0x89a5645cc68ea1b5, 0x00377df0d3902626),
+    P64::new(0x5f8aacf796c0cf0b, 0x00373622136907fa),
+    P64::new(0xf2e90a15e33edf99, 0x0036ef0c3b39b92f),
+    P64::new(0x8e99e5feb897c451, 0x0036915f47d55e6d),
+    P64::new(0xaca2eda38fb91695, 0x0036072cf3f866fd),
+    P64::new(0x5d9b737be5ea8b41, 0x0035d9b737be5ea8),
+    P64::new(0x4aefe1db93fd7cf7, 0x0035961559cc81c7),
+    P64::new(0xa0994ef20b3f8805, 0x0035531c897a4592),
+    P64::new(0x103890bda912822f, 0x00353ceebd3e98a4),
+    P64::new(0xb441659d13a9147d, 0x0034fad381585e5e),
+    P64::new(0x1e2134440c4c3f21, 0x00347884d1103130),
+    P64::new(0x263a27727a6883c3, 0x00340dd3ac39bf56),
+    P64::new(0x78e221472ab33855, 0x003351fdfecc140c),
+    P64::new(0x95eac88e82e6faff, 0x00333d72b089b524),
+    P64::new(0xf66c258317be8dab, 0x0033148d44d6b261),
+    P64::new(0x09ee202c7cb91939, 0x0032d7aef8412458),
+    P64::new(0x8d2fca1042a09ea3, 0x0032c3850e79c0f1),
+    P64::new(0x82779c856d8b8bf1, 0x00328766d59048a2),
+    P64::new(0x3879361cba8a223d, 0x00325fa18cb11833),
+    P64::new(0xf23f43639c3182a7, 0x00324bd659327e22),
+    P64::new(0xa03868fc474bcd13, 0x0032246e784360f4),
+    P64::new(0x651e78b8c5311a97, 0x0031afa5f1a33a08),
+    P64::new(0x8ffce639c00c6719, 0x00319c63ff398e70),
+    P64::new(0xf7b460754b0b61cf, 0x003162f7519a86a7),
+    P64::new(0x7b03f3359b8e63b1, 0x0030271fc9d3fc3c),
+    P64::new(0xa55c5326041eb667, 0x002ff104ae89750b),
+    P64::new(0x647f88ab896a76f5, 0x002fbb62a236d133),
+    P64::new(0x8fd971434a55a46d, 0x002f74997d2070b4),
+    P64::new(0x9fbf969958046447, 0x002ed84aa8b6fce3),
+    P64::new(0x9986feba69be3a81, 0x002e832df7a46dbd),
+    P64::new(0xa668b3e6d053796f, 0x002e0e0846857cab),
+    P64::new(0x97694e6589f4e09b, 0x002decfbdfb55ee6),
+    P64::new(0x37890c00b7721dbd, 0x002ddc876f3ff488),
+    P64::new(0x5ac094a235f37ea9, 0x002dbbc1d4c482c4),
+    P64::new(0x31cff775f2d5d65f, 0x002d8af0e0de0556),
+    P64::new(0xddad8e6b36505217, 0x002d4a7b7d14b30a),
+    P64::new(0x5a27df897062cd03, 0x002d2a85073bcf4e),
+    P64::new(0xe2396fe0fdb5a625, 0x002d1a9ab13e8be4),
+    P64::new(0xb352a4957e82317b, 0x002ceb1eb4b9fd8b),
+    P64::new(0xd8ab3f2c60c2ea3f, 0x002c8d503a79794c),
+    P64::new(0x6893f702f0452479, 0x002c404d708784ed),
+    P64::new(0x9686fdc182acf7e3, 0x002c31066315ec52),
+    P64::new(0x6854037173dce12f, 0x002c1297d80f2664),
+    P64::new(0x7f0ded1685c27331, 0x002c037044c55f6b),
+    P64::new(0xeeda72e1fe490b7d, 0x002be5404cd13086),
+    P64::new(0x9e7bfc959a8e6e53, 0x002bb845adaf0cce),
+    P64::new(0x49b314d6d4753dd7, 0x002b5f62c639f16d),
+    P64::new(0x2e8f8c5ac4aa1b3b, 0x002b07e6734f2b88),
+    P64::new(0xb8ef723481163d33, 0x002ace569d8342b7),
+    P64::new(0x6a2ec96a594287b7, 0x002a791d5dbd4dcf),
+    P64::new(0xdba41c6d13aab8c5, 0x002a4eff8113017c),
+    P64::new(0xc2adbe648dc3aaf1, 0x002a3319e156df32),
+    P64::new(0x87a2bade565f91a7, 0x002a0986286526ea),
+    P64::new(0x4d6fe8798c01f5df, 0x0029d29551d91e39),
+    P64::new(0x3791310c8c23d98b, 0x0029b7529e109f0a),
+    P64::new(0xf80e446b01228883, 0x00298137491ea465),
+    P64::new(0x9aed1436fbf500cf, 0x0029665e1eb9f9da),
+    P64::new(0x7839b54cc8b24115, 0x002909752e019a5e),
+    P64::new(0xc128c646ad0309c1, 0x0028ef35e2e5efb0),
+    P64::new(0x14de631624a3c377, 0x0028c815aa4b8278),
+    P64::new(0x3f7b9fe68b0ecbf9, 0x0028bb1b867199da),
+    P64::new(0x284ffd75ec00a285, 0x0028a13ff5d7b002),
+    P64::new(0x37803cb80dea2ddb, 0x00287ab3f173e755),
+    P64::new(0x86b63f7c9ac4c6fd, 0x00286dead67713bd),
+    P64::new(0x8b6851d1bd99b9d3, 0x002847bfcda6503e),
+    P64::new(0xb62fda77ca343b6d, 0x002808c1ea6b4777),
+    P64::new(0x1f0dc009e34383c9, 0x00278d0e0f23ff61),
+    P64::new(0x496dc21ddd35b97f, 0x002768863c093c7f),
+    P64::new(0xb0e96ce17090f82b, 0x0027505115a73ca8),
+    P64::new(0xaadf05acdd7d024d, 0x00274441a61dc1b9),
+    P64::new(0xcb138196746eafb5, 0x0026b5c166113cf0),
+    P64::new(0x347f523736755d61, 0x00269e65ad07b18e),
+    P64::new(0xd14a48a051f7dd0b, 0x002692c25f877560),
+    P64::new(0x474d71b1ce914d25, 0x002658fa7523cd11),
+    P64::new(0x386063f5e28c1f89, 0x0026148710cf0f9e),
+    P64::new(0x1db7325e32d04e73, 0x002609363b22524f),
+    P64::new(0xfef748d3893b880d, 0x0025d1065a1c1122),
+    P64::new(0x2f3351506e935605, 0x0025a48a382b863f),
+    P64::new(0x7a3637fa2376415b, 0x0025837190eccdbc),
+    P64::new(0x4ac525d2baa21969, 0x00256292e95d510c),
+    P64::new(0x3a11c16b42cd351f, 0x002541eda98d068c),
+    P64::new(0x6c7abde0049c2a11, 0x0024e15087fed8f5),
+    P64::new(0x54dad0303e069ac7, 0x0024c18b20979e5d),
+    P64::new(0xebf1ac9fdfe91433, 0x0024ac7b336de0c5),
+    P64::new(0xfafdda8237cec655, 0x0024a1fc478c60bb),
+    P64::new(0xdce3ff6e71ffb739, 0x002463801231c009),
+    P64::new(0xbed5737d6286db1b, 0x0024300fd506ed33),
+    P64::new(0xe479e431fe08b4df, 0x0023f314a494da81),
+    P64::new(0x9dd9b0dd7742f897, 0x0023cadedd2fad3a),
+    P64::new(0x8f09d7402c5a5e87, 0x00237b7ed2664a03),
+    P64::new(0x9216d5c4d958738d, 0x0023372967dbaf1d),
+    P64::new(0xb3139ba11d34ca63, 0x00231a308a371f20),
+    P64::new(0x47d54f7ed644afaf, 0x002306fa63e1e600),
+    P64::new(0x92a81d85cf11a1b1, 0x0022fd6731575684),
+    P64::new(0x754b26533253bdfd, 0x0022ea507805749c),
+    P64::new(0xbbe0efc980bfd467, 0x0022e0cce8b3d720),
+    P64::new(0xc0d8d594f024dca1, 0x0022b1887857d161),
+    P64::new(0x8238d43bcaac1a65, 0x00227977fcc49cc0),
+    P64::new(0x27779c1fae6175bb, 0x00225db37b5e5f4f),
+    P64::new(0xa746ca9af708b2c9, 0x0022421b91322ed6),
+    P64::new(0x93f3cd9f389be823, 0x0021f05b35f52102),
+    P64::new(0x5cb4a4c04c489345, 0x0021e75de5c70d60),
+    P64::new(0xbf6047743e85b6b5, 0x0021a01d6c19be96),
+    P64::new(0x61c147831563545f, 0x0021974a6615c81a),
+    P64::new(0xedb47c0ae62dee9d, 0x00213767697cf36a),
+    P64::new(0x0a3824386673a573, 0x00211d9f7fad35f1),
+    P64::new(0xa4a77d19e575a0eb, 0x0020fb7d9dd36c18),
+    P64::new(0xa2bee045e066c279, 0x0020e2123d661e0e),
+    P64::new(0xc23618de8ab43d05, 0x0020d135b66ae990),
+    P64::new(0x266b515216cb9f2f, 0x0020c8cded4d7a8e),
+    P64::new(0xe279edd9e9c2e85b, 0x0020b80b3f43ddbf),
+    P64::new(0xd0c591c221dc9c53, 0x002096b9180f46a6),
+    P64::new(0x06da8ee9c9ee7c21, 0x00207de7e28de5da),
+    P64::new(0x9dfebcaf4c27e8c3, 0x002054dec8cf1fb3),
+    P64::new(0x49aeff9f19dd6de5, 0x00204cb630b3aab5),
+    P64::new(0x86976a57a296e9c7, 0x00202428adc37beb),
+    P64::new(0xa3b9abf4872b84cd, 0x001fec0c7834def4),
+    P64::new(0x34fca6483895e6ef, 0x001fc46fae98a1d0),
+    P64::new(0x34b5a333988f873d, 0x001facda430ff619),
+    P64::new(0xd9dd4f19b5f17be1, 0x001f7e17dd8e15e5),
+    P64::new(0xb935b507fd0ce78b, 0x001f765a3556a4ee),
+    P64::new(0xb450f5540660e797, 0x001f66ea49d802f1),
+    P64::new(0x63ff82831ffc1419, 0x001f5f3800faf9c0),
+    P64::new(0x8992f718c22a32fb, 0x001f38f4e6c0f1f9),
+    P64::new(0x5f3253ad0d37e7bf, 0x001f0b8546752578),
+    P64::new(0x007c0ffe0fc007c1, 0x001f03ff83f001f0),
+    P64::new(0x4d8ebadc0c0640b1, 0x001ec853b0a3883c),
+    P64::new(0xe2729af831037bdb, 0x001ec0ee573723eb),
+    P64::new(0xb8f64bf30feebfe9, 0x001eaad38e6f6894),
+    P64::new(0xda93124b544c0bf5, 0x001e9c28a765fe53),
+    P64::new(0x9cf7ff0b593c539f, 0x001e94d8758c2003),
+    P64::new(0xd6bd8861fa0e07d9, 0x001e707ba8f65e68),
+    P64::new(0x5cfe75c0bd8ab891, 0x001e53a2a68f574e),
+    P64::new(0x43e808757c2e862b, 0x001e1380a56b438d),
+    P64::new(0x90caa96d595c9d93, 0x001dbf9f513a3802),
+    P64::new(0x8fd550625d07135f, 0x001db1d1d58bc600),
+    P64::new(0x76b010a86e209f2d, 0x001d9d358f53de38),
+    P64::new(0xecc0426447769b25, 0x001d81e6df6165c7),
+    P64::new(0xe381339caabe3295, 0x001d4bdf7fd40e30),
+    P64::new(0xd1b190a2d0c7673f, 0x001d452c7a1c958d),
+    P64::new(0xc3bce3cf26b0e7eb, 0x001d37cf9b902659),
+    P64::new(0x5f87e76f56c61ce3, 0x001d1d3a5791e97b),
+    P64::new(0xc06c6857a124b353, 0x001ce89fe6b47416),
+    P64::new(0x38c040fcba630f75, 0x001ce219f3235071),
+    P64::new(0xd078bc4fbd533b21, 0x001cd516dcf92139),
+    P64::new(0xde8e15c5dd354f59, 0x001cbb33bd1c2b8b),
+    P64::new(0xca61d53d7414260f, 0x001ca7e7d2546688),
+    P64::new(0xb56bf5ba8eae635d, 0x001c94b5c1b3dbd3),
+    P64::new(0x44a72cb0fb6e3949, 0x001c87f7f9c241c1),
+    P64::new(0x879839a714f45bcd, 0x001c6202706c35a9),
+    P64::new(0x02a8994fde5314b7, 0x001c5bb8a9437632),
+    P64::new(0xb971920cf2b90135, 0x001c174343b4111e),
+    P64::new(0x8a8fd0b7df9a6e8b, 0x001c04d0d3e46b42),
+    P64::new(0xb31f9a84c1c6eaad, 0x001bfeb00fbf4308),
+    P64::new(0x92293b02823c6d83, 0x001bec5dce0b202d),
+    P64::new(0xeee77ff20fe5ddcf, 0x001be03444620037),
+    P64::new(0x0e1ea0f6c496c11d, 0x001bce09c66f6fc3),
+    P64::new(0xfdf2d3d6f88ccb6b, 0x001ba40228d02b30),
+    P64::new(0xfa9d74a3457738f9, 0x001b9225b1cf8919),
+    P64::new(0xefc3ca3db71a5785, 0x001b864a2ff3f53f),
+    P64::new(0x8e2071718d0d6daf, 0x001b80604150e49b),
+    P64::new(0xbc0fdbfeb6cfabfd, 0x001b6eb1aaeaacf3),
+    P64::new(0x1eeab613e5e5aee9, 0x001b62f48da3c8cc),
+    P64::new(0x2d2388e90e9e929f, 0x001b516babe96092),
+    P64::new(0x81dbafba588ddb43, 0x001b2e9cef1e0c87),
+    P64::new(0x52eebc51c4799791, 0x001b1d56bedc849b),
+    P64::new(0x1c6bc4693b45a047, 0x001b0c267546aec0),
+    P64::new(0x06eee0974498874d, 0x001ae45f62024fa0),
+    P64::new(0xd85b7377a9953cb9, 0x001ad917631b5f54),
+    P64::new(0x4b6df412d4caf56f, 0x001ac83d18cb608f),
+    P64::new(0x6b8afbbb4a053493, 0x001aa6c7ad8c063f),
+    P64::new(0xcc5299c96ac7720b, 0x001a90a7b1228e2a),
+    P64::new(0xadce84b5c710aa99, 0x001a8027c03ba059),
+    P64::new(0x9d673f5aa3804225, 0x001a7533289deb89),
+    P64::new(0xe6541268efbce7f7, 0x001a2ed7ce16b49f),
+    P64::new(0xfcf41e76cf5be669, 0x0019fefc0a279a73),
+    P64::new(0x5c3eb5dc31c383cb, 0x0019e4b0cd873b5f),
+    P64::new(0x301832d11d8ad6c3, 0x0019cfcdfd60e514),
+    P64::new(0x2e9c0942f1ce450f, 0x0019c56932d66c85),
+    P64::new(0x97f3f2be37a39a5d, 0x0019b5e1ab6fc7c2),
+    P64::new(0xe8b7d8a9654187c7, 0x0019b0b8a62f2a73),
+    P64::new(0xb5d024d7da5b1b55, 0x0019a149fc98942c),
+    P64::new(0xb8ba9d6e7ae3501b, 0x001969517ec25b85),
+    P64::new(0xf50865f71b90f1df, 0x00194b3083360ba8),
+    P64::new(0x739c1682847df9e1, 0x00194631f4bebdc1),
+    P64::new(0xc470a4d842b90ed1, 0x00191e84127268fd),
+    P64::new(0x1fb1be11698cc409, 0x00190adbb543984f),
+    P64::new(0xd8d5512a7cd35d15, 0x001901130bd18200),
+    P64::new(0xa5496821723e07f9, 0x0018e3e6b889ac94),
+    P64::new(0xbcc8c6d7abaa8167, 0x0018c233420e1ec1),
+    P64::new(0x52c396c95eb619a1, 0x0018aa5872d92bd6),
+    P64::new(0x6eb7e380878ec74b, 0x0018a5989945ccf9),
+    P64::new(0x3d5513b504537157, 0x00189c1e60b57f60),
+    P64::new(0x314391f8862e948f, 0x0018893fbc8690b9),
+    P64::new(0xdc0b17cfcd81f5dd, 0x00187b2bb3e1041c),
+    P64::new(0x2f6bea3ec89044b3, 0x00186d27c9cdcfb8),
+    P64::new(0xce13a05869f1b57f, 0x001863d8bf4f2c1c),
+    P64::new(0x7593474e8ace3581, 0x00185f33e2ad7593),
+    P64::new(0x07fc329295a05e4d, 0x001855ef75973e13),
+    P64::new(0xb05377cba4908d23, 0x001848160153f134),
+    P64::new(0xe7b2131a628aa39b, 0x001835b72e6f0656),
+    P64::new(0x9031dbed7de01527, 0x00182c922d83eb39),
+    P64::new(0x76844b1c670aa9a9, 0x0018280243c0365a),
+    P64::new(0x6a03f4533b08915f, 0x00181a5cd5898e73),
+    P64::new(0x1dbca579db0a3999, 0x001803c0961773aa),
+    P64::new(0x002ffe800bffa003, 0x0017ff4005ffd001),
+    P64::new(0x478ab1a3e936139d, 0x0017e8d670433edb),
+    P64::new(0x66e722bc4c5cc095, 0x0017d7066cf4bb5d),
+    P64::new(0x7a8f63c717278541, 0x0017ce285b806b1f),
+    P64::new(0xdf6eee24d292bc2f, 0x0017af52cdf27e02),
+    P64::new(0x9fc20d17237dd569, 0x0017997d47d01039),
+    P64::new(0xcdf9932356bda2ed, 0x00177f7ec2c6d0ba),
+    P64::new(0x97b5e332e80f68d7, 0x00177b2f3cd00756),
+    P64::new(0x46eee26fd875e2e5, 0x00176e4a22f692a0),
+    P64::new(0x3548a8e65157a611, 0x001765b94271e11b),
+    P64::new(0xc288d03be9b71e3b, 0x001761732b044ae4),
+    P64::new(0x8151186db38937ab, 0x00173f7a5300a2bc),
+    P64::new(0x7800b910895a45f1, 0x001722112b48be1f),
+    P64::new(0xaee0b024182eec3d, 0x001719b7a16eb843),
+    P64::new(0x96323eda173b5713, 0x00170d3c99cc5052),
+    P64::new(0x0ed0dbd03ae77c8b, 0x0016fcad7aed3bb6),
+    P64::new(0xf73800b7828dc119, 0x0016f051b8231ffd),
+    P64::new(0x1b61715ec22b7ca5, 0x0016e81beae20643),
+    P64::new(0xa8533a991ead64bf, 0x0016c3721584c1d8),
+    P64::new(0x7f6c7290e46c2e77, 0x0016b34c2ba09663),
+    P64::new(0x6325e8d907b01db1, 0x00169f3ce292ddcd),
+    P64::new(0x28909f70152a1067, 0x00169344b2220a0d),
+    P64::new(0xea7077af0997a0f5, 0x001687592593c1b1),
+    P64::new(0x7e605cad10c32e6d, 0x00167787f1418ec9),
+    P64::new(0x471b33570635b38f, 0x001663e190395ff2),
+    P64::new(0xab559fa997a61bb3, 0x00164c7a4b6eb5b3),
+    P64::new(0xad4bdae562bddab9, 0x0016316a061182fd),
+    P64::new(0x055e1b2f2ed62f45, 0x001629ba914584e4),
+    P64::new(0x03cd328b1a2dca9b, 0x00161e3d57de21b2),
+    P64::new(0xd28f4e08733218a9, 0x001612cc01b977f0),
+    P64::new(0xb6800b077f186293, 0x00160efe30c525ff),
+    P64::new(0x6fbd138c3fd9c207, 0x0015da45249ec5de),
+    P64::new(0xb117ccd12ae88a89, 0x0015d68ab4acff92),
+    P64::new(0x2f1a1a044046bceb, 0x0015c3f989d1eb15),
+    P64::new(0x548aba0b060541e3, 0x0015b535ad11b8f0),
+    P64::new(0xcf4e808cea111b2f, 0x0015addb3f424ec1),
+    P64::new(0xdbec1b4fa855a475, 0x00159445cb91be6b),
+    P64::new(0xe3f794eb600d7821, 0x00158d0199771e63),
+    P64::new(0x34fae0d9a11f7c59, 0x00157e87d9b69e04),
+    P64::new(0xf006b0ccbbac085d, 0x001568f58bc01ac3),
+    P64::new(0x3f45076dc3114733, 0x00155e3c993fda9b),
+    P64::new(0xeef49bfa58a1a1b7, 0x001548eacc5e1e6e),
+    P64::new(0x12c4218bea691fa3, 0x001541d8f91ba6a7),
+    P64::new(0xbc7504e3bd5e64f1, 0x00153747060cc340),
+    P64::new(0x4ee21c292bb92fad, 0x001514569f93f7c4),
+    P64::new(0x34338b7327a4bacf, 0x00150309705d3d79),
+    P64::new(0x3fe5c0833d6fccd1, 0x0014ff97020cf5bf),
+    P64::new(0xb1e70743535203c1, 0x0014e42c114cf47e),
+    P64::new(0xefbb5dcdfb4e43d3, 0x0014b835bdcb6447),
+    P64::new(0xca68467ca5394f9f, 0x0014b182b53a9ab7),
+    P64::new(0x8c51c081408b97a1, 0x0014ae2ad094a3d3),
+    P64::new(0x3275a899dfa5dd65, 0x00149a320ea59f96),
+    P64::new(0x9e674cb62e1b78bb, 0x001490441de1a2fb),
+    P64::new(0xa37ff5bb2a998d47, 0x001489aacce57200),
+    P64::new(0x792a999db131a22b, 0x001475f82ad6ff99),
+    P64::new(0x1b48841bc30d29b9, 0x00146c2cfe53204f),
+    P64::new(0xf06721d2011d3471, 0x00145f2ca490d4a1),
+    P64::new(0x93fd2386dff85ebd, 0x001458b2aae0ec87),
+    P64::new(0x4ce72f54c07ed9b5, 0x00144bcb0a3a3150),
+    P64::new(0xd6d0fd3e71dd827b, 0x001428a1e65441d4),
+    P64::new(0x856405fb1eed819d, 0x00142575a6c210d7),
+    P64::new(0x8ea8aceb7c443989, 0x00141f2025ba5c46),
+    P64::new(0x34a13026f62e5873, 0x00141bf6e35420fd),
+    P64::new(0x1eea0208ec0af4f7, 0x001409141d1d313a),
+    P64::new(0x63679853cea598cb, 0x0013dd8bc19c3513),
+    P64::new(0xc30b3ebd61f2d0ed, 0x0013da76f714dc8f),
+    P64::new(0x7eb9037bc7f43bc3, 0x0013d13e50f8f49e),
+    P64::new(0xa583e6f6ce016411, 0x0013c80e37ca3819),
+    P64::new(0xf1938d895f1a74c7, 0x0013bee69fa99ccf),
+    P64::new(0x80cf1491c1e81e33, 0x0013b8d0ede55835),
+    P64::new(0x3c0f12886ba8f301, 0x0013afb7680bb054),
+    P64::new(0x0e4b786e0dfcc5ab, 0x0013acb0c3841c96),
+    P64::new(0x672684c93f2d41ef, 0x00139a9c5f434fde),
+    P64::new(0xe00757badb35c51b, 0x0013949cf33a0d9d),
+    P64::new(0xd6d84afe66472edf, 0x001382b4a00c31b0),
+    P64::new(0xfbbc0eedcbbfb6e1, 0x00137fbbc0eedcbb),
+    P64::new(0x250f43aa08a84983, 0x001370ecf047b069),
+    P64::new(0x04400e927b1acaa5, 0x00136df9790e3155),
+    P64::new(0x56572be34b9d3215, 0x0013567dd8defd5b),
+    P64::new(0x87964ef7781c62bf, 0x0013539261fdbc34),
+    P64::new(0x29ed84051c06e9af, 0x00133c564292d28a),
+    P64::new(0xb00acd11ed3f87fd, 0x001333ae178d6388),
+    P64::new(0x06307881744152d9, 0x0013170ad00d1fd7),
+    P64::new(0x7a786459f5c1ccc9, 0x0013005f01db0947),
+    P64::new(0x1308125d74563281, 0x0012f51d40342210),
+    P64::new(0x395310a480b3e34d, 0x0012ef815e4ed950),
+    P64::new(0x35985baa8b202837, 0x0012ecb4abccd827),
+    P64::new(0x96304a6e052b3223, 0x0012e71dc1d3d820),
+    P64::new(0xbd8265fc9af8fd45, 0x0012e45389a16495),
+    P64::new(0x1b6d0b383ec58e0b, 0x0012c5d9226476cc),
+    P64::new(0xc21a7c3b68b28503, 0x0012badc391156fd),
+    P64::new(0x236fa180fbfd6007, 0x0012aa78e412f522),
+    P64::new(0xc42accd440ed9595, 0x0012a251f5f47fd1),
+    P64::new(0x7acf7128236ba3f7, 0x001294cb85c53534),
+    P64::new(0xf909367a987b9c79, 0x0012921963beb65e),
+    P64::new(0xb64efb252bfba705, 0x00128cb777c69ca8),
+    P64::new(0x980d4f5a7e4cd25b, 0x001284aa6cf07294),
+    P64::new(0xe1ecc4ef27b0c37d, 0x001281fcf6ac7f87),
+    P64::new(0x9111aebb81d72653, 0x001279f937367db9),
+    P64::new(0x8951f985cb2c67ed, 0x00126cad0488be94),
+    P64::new(0xc439d4fc54e0b5d7, 0x00126a06794646a2),
+    P64::new(0xe857bf31896d533b, 0x00125a2f2bcd3e95),
+    P64::new(0xb614bb4cb5023755, 0x00124d108389e6b1),
+    P64::new(0x938a89e5473bf1ff, 0x00124a73083771ac),
+    P64::new(0xeac481aca34de039, 0x00123d6acda0620a),
+    P64::new(0x14b961badf4809a7, 0x00122b4b2917eafd),
+    P64::new(0x76784fecba352435, 0x00122391bfce1e2f),
+    P64::new(0xefa689bb58aef5e1, 0x00121e6f1ea579f2),
+    P64::new(0xb2b2c4db9c3a8197, 0x001216c09e471568),
+    P64::new(0x2503bc992279f8cf, 0x00120c8cb9d93909),
+    P64::new(0xd2ab9aec5ca1541d, 0x001204ed58e64ef9),
+    P64::new(0x3e78ba1460f99af3, 0x0011fd546578f00c),
+    P64::new(0x0a01426572cfcb63, 0x0011e9310b8b4c9c),
+    P64::new(0xbea857968f3cbd67, 0x0011da3405db9911),
+    P64::new(0x78db213eefe659e9, 0x0011d7b6f4eb055d),
+    P64::new(0x963e8541a74d35f5, 0x0011d2bee748c145),
+    P64::new(0x9e22d152776f2e43, 0x0011c1706ddce7a7),
+    P64::new(0x05d10d39d1e1f291, 0x0011ba0fed2a4f14),
+    P64::new(0x374468dccaced1dd, 0x0011b528538ed64a),
+    P64::new(0x8d145c7d110c5ad5, 0x0011ab61404242ac),
+    P64::new(0x3251a39f5acb5737, 0x00119f378ce81d2f),
+    P64::new(0xa66e50171443506f, 0x001195889ece79da),
+    P64::new(0x124f69ad91dd4cbd, 0x00118e4c65387077),
+    P64::new(0xec24f8f2a61a2793, 0x001187161d70e725),
+    P64::new(0xb472148e656b7a51, 0x00116cd6d1c85239),
+    P64::new(0x0adf9570e1142f07, 0x001165bbe7ce86b1),
+    P64::new(0x89bf33b065119789, 0x0011635ee344ce36),
+    P64::new(0x8f0149803cb291eb, 0x0011579767b6d679),
+    P64::new(0x8334b63afd190a31, 0x00114734711e2b54),
+    P64::new(0x920908d50d6aba7d, 0x0011428b90147f05),
+    P64::new(0x57d8b018c5a33d53, 0x00113b92f3021636),
+    P64::new(0xea1773092dc27ee5, 0x001126cabc886884),
+    P64::new(0xcae5f38b7bf2e00f, 0x0011247eb1b85976),
+    P64::new(0x2bd02df34f695349, 0x0011190bb01efd65),
+    P64::new(0xddfecd5be62e2eb7, 0x0011091de0fd679c),
+    P64::new(0xdbf849ebec96c4a3, 0x001104963c7e4e0b),
+    P64::new(0xda31d4d0187357c5, 0x00110253516420b0),
+    P64::new(0xe34e21cc2d5418a7, 0x0010f70db7c41797),
+    P64::new(0x68ca5137a9e574ad, 0x0010e75ee2bf9ecd),
+    P64::new(0x3eaa0d0f804bfd19, 0x0010e2e91c6e0676),
+    P64::new(0x554fb753cc20e9d1, 0x0010da049b9d428d),
+    P64::new(0x797afcca1300756b, 0x0010c6248fe3b1a2),
+    P64::new(0x8b8d950b52eeea77, 0x0010c1c03ed690eb),
+    P64::new(0xfb6cd166acabc185, 0x0010bb2e1379e3a2),
+    P64::new(0x4eb6c5ed9437a7af, 0x0010b8fe7f61228e),
+    P64::new(0xd1eddbd91b790cdb, 0x0010b4a10d60a4f7),
+    P64::new(0x93d714ea4d8948e9, 0x0010ae192681ec0f),
+    P64::new(0x3ca13ed8145188d3, 0x0010abecfbe5b0ae),
+    P64::new(0x829086016da89c57, 0x00109eefd568b96d),
+    P64::new(0xd7da1f432124a543, 0x00109a9ff178b40c),
+    P64::new(0x7ead5581632fb07f, 0x00108531e22f9ff9),
+    P64::new(0x35443837f63ec3bd, 0x00106ddec1af4417),
+    P64::new(0x89e2b200e5519461, 0x0010614174a4911d),
+    P64::new(0xe9ae44f0b7289c0b, 0x00105f291f0448e7),
+    P64::new(0x94387a277b9fa817, 0x00105afa0ef32891),
+    P64::new(0xc84f1a58abfc2c25, 0x001054b777bd2530),
+    P64::new(0x71101d8e3c83377b, 0x00104e79a97fb69e),
+    P64::new(0xc024abe5c50ba69d, 0x00104c661eafd845),
+    P64::new(0x15de4eb365a65d73, 0x0010462ea939c933),
+    P64::new(0x09ed28a76bcca931, 0x00102f8baa442836),
+    P64::new(0x816bffbf4a00205b, 0x00102d7ff7e94004),
+    P64::new(0x1f5c71543d558069, 0x0010275ff9f13c02),
+    P64::new(0xf25c64d0ec53b859, 0x001017213fcbb4d3),
+    P64::new(0x96c02c2ef1e0ff0f, 0x00101112234579d1),
+    P64::new(0x19a804816870a333, 0x00100501907d271c),
+    P64::new(0x6de49add0971c555, 0x00100300901b0510),
+    P64::new(0x528087e684c71aab, 0x000ffd008fe5050f),
+    P64::new(0xa94152c269bcdeef, 0x000ff10e02dd5084),
+    P64::new(0x0379450a3c2b6bdf, 0x000fe13b9c80c67f),
+    P64::new(0xd2cd38bafe5373e1, 0x000fdf4384be37ad),
+    P64::new(0xc29df2bea71d8bad, 0x000fdb54cbe8766e),
+    P64::new(0xc15862775f302e83, 0x000fd5725ca6ff32),
+    P64::new(0x1016af2fe55ede09, 0x000fc7c84684c6fb),
+    P64::new(0x3d26dbd9d1910715, 0x000fc3e5265dbaa8),
+    P64::new(0x621dab2dfaf3dfbf, 0x000fc1f44e0cae12),
+    P64::new(0xb6f1d7ac287338b1, 0x000fb0921c50a7af),
+    P64::new(0x8d9e9f0c3f9e7fd9, 0x000f999fd70cbc6b),
+    P64::new(0x60a93f8762e914bb, 0x000f9023fd5339d0),
+    P64::new(0xb14371f247c159c9, 0x000f8a78ce671475),
+    P64::new(0x6dd3b484471d4eb3, 0x000f8895fee86574),
+    P64::new(0xcd172f4701c1684d, 0x000f7f2ecb084b10),
+    P64::new(0x0372e686ed8bb537, 0x000f7d4eb7d10c29),
+    P64::new(0xbc07f7ca65c5b071, 0x000f73f52277a3c3),
+    P64::new(0xab2b6170c3f78d9b, 0x000f7217c598961c),
+    P64::new(0xf3d74f461fe6f5b5, 0x000f68cbb1448f42),
+    P64::new(0xdbc13f4b31f3230b, 0x000f633d0276e4c5),
+    P64::new(0xd1420716e3f1572d, 0x000f6163ac20ec79),
+    P64::new(0xd5be2fd4d805464f, 0x000f582ba2bc16c6),
+    P64::new(0xc68b97c136943851, 0x000f5654f43290a0),
+    P64::new(0x9e27918af7cfb473, 0x000f4d2a23810bc6),
+    P64::new(0x5ec8ab6c36ac7f41, 0x000f47af4d6a2f27),
+    P64::new(0x964076331dd90979, 0x000f4066f2b6e652),
+    P64::new(0x30198eff77b002d7, 0x000f2555048e3a92),
+    P64::new(0x3af7cb9583ece011, 0x000f1c64588a5bf6),
+    P64::new(0x34ce06f643d9883b, 0x000f1a9be09cb411),
+    P64::new(0x79f767e528708c55, 0x000f11b7d5259d39),
+    P64::new(0x185332d2ef2313cd, 0x000f0aa284e7f802),
+    P64::new(0x43b611b84c8332a3, 0x000f0556e5e3b7f2),
+    P64::new(0xc2e215e4f43bb63d, 0x000efc8bcbc808e5),
+    P64::new(0xf94b9dd22ce44e97, 0x000eecd1a690efbb),
+    P64::new(0xd895834a1db166a5, 0x000ee79aed6d65f2),
+    P64::new(0x347d2f16d19b8d09, 0x000edd386114d83a),
+    P64::new(0x1b54d4dc45b7d98d, 0x000ed2e44366e5e2),
+    P64::new(0x117ac30d9a044877, 0x000ed12cf8e17f64),
+    P64::new(0x0e10b78a67a526e9, 0x000ec1cd284b2b2d),
+    P64::new(0x92da68a818688a9f, 0x000ebcb44cadda1e),
+    P64::new(0xcf2b6c87f741f84b, 0x000eb9505943771d),
+    P64::new(0xd264f9bd41e18ed9, 0x000eb43d57efeadc),
+    P64::new(0x733cbeaa97166d8f, 0x000eaf2dd4c00b03),
+    P64::new(0xc9f475b021d22e81, 0x000ea0141c1ba6a6),
+    P64::new(0x731f76f2ec4c852b, 0x000e9e68805f05a7),
+    P64::new(0xdaf6f0c978f69945, 0x000e96142b87e431),
+    P64::new(0x749c8ad20c61ec93, 0x000e8a7acd811b8c),
+    P64::new(0x09307ff8bd3c1261, 0x000e8587db3e001d),
+    P64::new(0x334a69fb5a486e2d, 0x000e823d186d44dc),
+    P64::new(0x1f36c7bf31578617, 0x000e8098463ee194),
+    P64::new(0x31ebbcc279ea6103, 0x000e7d4fbfb3ee1d),
+    P64::new(0x42e2aad119f466eb, 0x000e69bba6981ffa),
+    P64::new(0x106ec05a0ab1450d, 0x000e681c5cf7d707),
+    P64::new(0xb1b38db92a99e731, 0x000e5e684930e334),
+    P64::new(0x784ae377e67071e7, 0x000e5993247dc92d),
+    P64::new(0x3e9e1471ba6671d7, 0x000e4cbfee201016),
+    P64::new(0x82c29b59d4d73d0f, 0x000e465ee7daf979),
+    P64::new(0xc23dd07128b5525d, 0x000e4199de07af5c),
+    P64::new(0x4d4e5ce0e9245133, 0x000e3cd8031d4f40),
+    P64::new(0xc8fd1057c09f8cc5, 0x000e2ea56c157eb2),
+    P64::new(0xea1516e94f394035, 0x000e221e5d4d3c73),
+    P64::new(0xb5e3319c564ee9df, 0x000e208f09a841c7),
+    P64::new(0x126a69f90d822d8b, 0x000e1d716a945161),
+    P64::new(0x501ed6348857aa19, 0x000e18c78ec8fd4d),
+    P64::new(0xde344a324eee1c83, 0x000e173a4a162079),
+    P64::new(0x1dd9690cb2c406d1, 0x000e1294881bb494),
+    P64::new(0x08d6c5178d5e4387, 0x000e0df1d5f24661),
+    P64::new(0x4cea4050a3e8fdc1, 0x000e063ec7f50b1e),
+    P64::new(0xc114a06acc83f777, 0x000e01a4313dc53d),
+    P64::new(0x20b060ebc0ea01db, 0x000df8780f47c350),
+    P64::new(0xfe50045acb78c99f, 0x000def57e8eb9666),
+    P64::new(0x291a68705b196e91, 0x000de1bdf3f63d46),
+    P64::new(0xc1042c724273e2bb, 0x000de03cb5099809),
+    P64::new(0x2cee680bb165b7c9, 0x000ddbbaecc84bc9),
+    P64::new(0xfd2ff9f12e0776d5, 0x000dd8bb5ca73db6),
+    P64::new(0x166a5da63af2cc6f, 0x000dcb4d529a6e07),
+    P64::new(0xedd16a5930408d27, 0x000dc55da73dea60),
+    P64::new(0x2adf30c26528844f, 0x000db3ad2585011f),
+    P64::new(0x9a48d6572b5eec7b, 0x000db0becf636a79),
+    P64::new(0x6e8bf2877503cb9d, 0x000daf481ca6fefb),
+    P64::new(0xea27a191a7045389, 0x000dac5ba7565dae),
+    P64::new(0x6eb091f34dd45d3f, 0x000da7fb4e419d19),
+    P64::new(0xdc8a6cabb2937d41, 0x000da6867a88d327),
+    P64::new(0xbc2f04f254922a05, 0x000d9dd005f50b02),
+    P64::new(0x41431f4d6eb38631, 0x000d9aeb01f763f7),
+    P64::new(0x7bd717435a08291f, 0x000d90d31dd5804a),
+    P64::new(0x4232df9c91fc1a55, 0x000d7b6453358f31),
+    P64::new(0xa4651e1d5382eab7, 0x000d744e69d900e4),
+    P64::new(0x7cfb5409de4cf3c5, 0x000d7011a317260e),
+    P64::new(0xcdd636fb068b9929, 0x000d67a0126e7c19),
+    P64::new(0xee8f95e740462c97, 0x000d5dd39e775bd7),
+    P64::new(0x490f97b3a758b4a5, 0x000d59a4f2990168),
+    P64::new(0x641431563c441287, 0x000d52b24cb6269d),
+    P64::new(0xb743dad3ec45916b, 0x000d4a6571da4f04),
+    P64::new(0x7b188be8f55c878d, 0x000d49044eac6581),
+    P64::new(0xd805648b2ca54ef9, 0x000d4642e40d1129),
+    P64::new(0x76dbe6eef60123af, 0x000d4222e81fe723),
+    P64::new(0x3711525e6a9e8867, 0x000d3ca6e8c89f41),
+    P64::new(0x85c2215cb383d8f5, 0x000d388ce29d4edc),
+    P64::new(0xe58f554c89825857, 0x000d31bc7b7d8013),
+    P64::new(0x8fbd3b17c01dacd9, 0x000d306071c13fd5),
+    P64::new(0x4c8c39dc7aedee65, 0x000d2da935479b1a),
+    P64::new(0x653ac6dda86cd3b3, 0x000d2430aa043597),
+    P64::new(0x0d61c6791a9c2c81, 0x000d2025bc6c7db7),
+    P64::new(0xb627a30090354237, 0x000d1c1d4ad1732b),
+    P64::new(0x83a89a539c527c23, 0x000d196e5f46f8c8),
+    P64::new(0x28c8c09330e90d71, 0x000d156a0c9293e8),
+    P64::new(0xee1178d27b1f029b, 0x000d1413d26e0aee),
+    P64::new(0xcecc740b37860ab5, 0x000d0d68c6a4128f),
+    P64::new(0x79736fde910c485f, 0x000d0c142eaf3837),
+    P64::new(0x6873d51f2487234f, 0x000d01792ab9d70d),
+    P64::new(0x2a112180614fb973, 0x000cf990317775bc),
+    P64::new(0xcb04cea98508f4eb, 0x000cf44f8c38790a),
+    P64::new(0xc2fcd2c527e28d7d, 0x000ce88d96d10e45),
+    P64::new(0x980203ee10393c69, 0x000ce5f39b07e906),
+    P64::new(0x3fa90a1d7d75681f, 0x000ce20e98148847),
+    P64::new(0xdbf3bfefef217cc3, 0x000cda4b9c30ccd7),
+    P64::new(0x66a17fd3087b41e5, 0x000cd9015ae32495),
+    P64::new(0x962195d496fbbd3b, 0x000cd524244aca36),
+    P64::new(0xc705a86155443e49, 0x000cd14940099cf6),
+    P64::new(0x3f298ee0be6febff, 0x000ccd70ac089a07),
+    P64::new(0xaa99b084e62fa613, 0x000cbb9c535c4371),
+    P64::new(0x1f000cb7d0b46fe1, 0x000cb7d0b46fe0ff),
+    P64::new(0x9ed7858637c9b2cf, 0x000caefe5d7135f4),
+    P64::new(0x4d871aaf27c106fb, 0x000cac7b5f00f0cd),
+    P64::new(0x2e6a467cdc75a4f3, 0x000ca7785ceddbea),
+    P64::new(0xe9d938fb696dde8d, 0x000ca13a2a86e1db),
+    P64::new(0x40ec71b0b1554485, 0x000c9c4009753007),
+    P64::new(0x3aae12f861e5f3e9, 0x000c94d02e64bfab),
+    P64::new(0xa97565873959f843, 0x000c89b8c9c875ef),
+    P64::new(0x0b5a960c09fbca8f, 0x000c87447737277e),
+    P64::new(0x463fe3d268012c91, 0x000c860aaa2514e3),
+    P64::new(0xe59a6bd5f5ee1bdd, 0x000c8397c813f1b9),
+    P64::new(0x6542e84d7775ce45, 0x000c74fa805d6d56),
+    P64::new(0x8b6eef58fd9effa9, 0x000c6db8a1f5cdfe),
+    P64::new(0x58993dbb9f98075f, 0x000c6a1add9e2398),
+    P64::new(0x2997955a810acf61, 0x000c68e6be826648),
+    P64::new(0x76e3d2f5077db451, 0x000c5f4e25fc9df0),
+    P64::new(0xb37c1d2867e30907, 0x000c5bb8bf2ad1cd),
+    P64::new(0x53ce6e09bd8d8695, 0x000c58256b316ced),
+    P64::new(0x39db291ea2a6b0e3, 0x000c4fd5ad917b5b),
+    P64::new(0xddd265ab9c58847d, 0x000c49ecb3ea4d7a),
+    P64::new(0x5beca8562dddd0cb, 0x000c41b00b7d950a),
+    P64::new(0xb69031c153ddbed7, 0x000c3f57990b87a1),
+    P64::new(0xd03c2271b42a6fcd, 0x000c2ddcb31250f8),
+    P64::new(0xcd6fd19e63e40ea3, 0x000c2a63b3651432),
+    P64::new(0xf7687aa8e4fd7bf1, 0x000c26ecae1db72e),
+    P64::new(0x649dfda112a272a7, 0x000c2377a18c051e),
+    P64::new(0xecf7866a56d526df, 0x000c1ede9efcec29),
+    P64::new(0x72bbf1cfdaebfead, 0x000c1b6e258d13a0),
+    P64::new(0x55f6a48df7055719, 0x000c19243f5399bb),
+    P64::new(0x80060bffcfa00183, 0x000c17ff9f400305),
+    P64::new(0x8a104f309919b087, 0x000c112865703b94),
+    P64::new(0x98fa7db7652f6a15, 0x000c0dbfaea33225),
+    P64::new(0x5d7d1b3df70f7ac1, 0x000c0b7af12ddfb9),
+    P64::new(0x16ab7b5e04cc1f6b, 0x000c0a58e464462c),
+    P64::new(0x78a5bfd2e5ececf9, 0x000c06f40512eef2),
+    P64::new(0x6506392e171d869f, 0x000bfa9275a2b247),
+    P64::new(0xc3fc12e221ef146d, 0x000bf7367402cdf0),
+    P64::new(0xf8aa132822c33657, 0x000bf61833f4f921),
+    P64::new(0x894496574f536f43, 0x000bf3dc543a74a1),
+    P64::new(0x8b2546b08fb4cbd5, 0x000be9d9302a7115),
+    P64::new(0x043bbb561bd1aa7f, 0x000be8bd6e051e01),
+    P64::new(0x2412c7cc4ea7a12b, 0x000be6868804d5a6),
+    P64::new(0x6f0bd406dd71696f, 0x000bdfe6c4359f0e),
+    P64::new(0xad475c6988d54b71, 0x000bdeccdb0b5c3a),
+    P64::new(0xd812e5d48dbbba27, 0x000bdb8058ee429a),
+    P64::new(0x22aaca437ba04893, 0x000bd94e5c1b371f),
+    P64::new(0xdba6ff1fecd5f09d, 0x000bcb1d293b1af3),
+    P64::new(0x13016d3396286773, 0x000bc7db8db0c1a5),
+    P64::new(0xc746494631bcfa41, 0x000bc49bbdfd2662),
+    P64::new(0xd14888565bf6a10d, 0x000bc2723240f402),
+    P64::new(0xc002ef885f0adf05, 0x000bbe217c2b7c13),
+    P64::new(0xe5a04da7fee6ade7, 0x000bb8c10aab27b2),
+    P64::new(0xc114ce5468593bc7, 0x000ba7ad528a7e79),
+    P64::new(0x0bb6747dd7f577b7, 0x000b9f3611b48c5e),
+    P64::new(0x395ce5a20f285839, 0x000b9e2806e5e7c4),
+    P64::new(0x6eee8be66e8618ef, 0x000b9aff0c4913fe),
+    P64::new(0x52acf64297f1241b, 0x000b98e4aedd581c),
+    P64::new(0x361dcc48a364093d, 0x000b97d7c94b7dc2),
+    P64::new(0x342d6f475d72e629, 0x000b95be902d9d9e),
+    P64::new(0x5e978bd46410d413, 0x000b94b23c872b90),
+    P64::new(0xcc3433d75ba015ad, 0x000b8f77714d15a1),
+    P64::new(0x1c83b7628458d4fb, 0x000b882d0beff6a1),
+    P64::new(0xf9ca45637e38f809, 0x000b850ff9852703),
+    P64::new(0xcbed792ffaf6b115, 0x000b82fd86db8806),
+    P64::new(0x9abd961d8c0e8c8d, 0x000b7edadd32f76c),
+    P64::new(0xe69572fa659340af, 0x000b79b3b4df3b7b),
+    P64::new(0x9187e7483a6436fd, 0x000b769e6d59833f),
+    P64::new(0x1e9c726993bed9d9, 0x000b6c636b5141ff),
+    P64::new(0x243554db91976365, 0x000b6a59ceae8801),
+    P64::new(0x04d06ff994c0088f, 0x000b6955461e38f7),
+    P64::new(0x25b76abcb74889dd, 0x000b6648c2dc6bc2),
+    P64::new(0x3a409642893c779b, 0x000b572282260209),
+    P64::new(0x8f8f620d8bc0c927, 0x000b552072bde889),
+    P64::new(0x6f9f196b3369855f, 0x000b511e7552f9c4),
+    P64::new(0x92a522bb0638ed99, 0x000b4c1ff34a5c0e),
+    P64::new(0x96270f1efdd7004f, 0x000b4922f58d4aa2),
+    P64::new(0xb4844b380fdaa79d, 0x000b46278c16b967),
+    P64::new(0x108936aa5f9c1495, 0x000b42301cd99b49),
+    P64::new(0x0b60f606f104c9eb, 0x000b3f385dd77e4e),
+    P64::new(0xc663dfe8263b302f, 0x000b394d8ef8f0f6),
+    P64::new(0xc91a280b9110b15b, 0x000b375601507c14),
+    P64::new(0x0904287118d10969, 0x000b3463f76be376),
+    P64::new(0x160d36a5d31bf553, 0x000b3368f6c4a07c),
+    P64::new(0xe84f5fda3c67ad21, 0x000b3078fc1c25f0),
+    P64::new(0xbd85701f72d4b6ed, 0x000b2e84854e93e5),
+    P64::new(0x4c50cf5924dee1c3, 0x000b2b971aa909a4),
+    P64::new(0x2455aaf1633bb6e5, 0x000b2a9da39d6bc8),
+    P64::new(0xd775b39f549b8ac7, 0x000b25c0dc29a0fc),
+    P64::new(0x87fcdda7a252cb49, 0x000b24c8698449a7),
+    P64::new(0x53df2e3bd254a739, 0x000b1d0ae579aefe),
+    P64::new(0x8915e69623a5f7ef, 0x000b1a2698ea2f9e),
+    P64::new(0x1ef24c80742dd08b, 0x000b108dc4186078),
+    P64::new(0xb4d87aaa6fb1e897, 0x000b0ea463b00212),
+    P64::new(0x788573e8b92dbbfb, 0x000b08ec37007962),
+    P64::new(0x02527b137b0878c1, 0x000b024778cc023c),
+    P64::new(0x1870a7c8dee9f4f5, 0x000af515df36a88e),
+    P64::new(0x39b99e40910a224b, 0x000af24635f6561e),
+    P64::new(0x45821c0abd4df247, 0x000ae8f1b92baeaf),
+    P64::new(0x10fe2b2f50e02fb3, 0x000ae715eee11f8e),
+    P64::new(0x5762b90c043f0345, 0x000adec0b0a3bb36),
+    P64::new(0x82a67b9193b27bbd, 0x000adb10aa4c956f),
+    P64::new(0xa6e914e28ec37693, 0x000ad84e49752245),
+    P64::new(0x835d9a4facaf445f, 0x000ad6782597f0c2),
+    P64::new(0x48def8175884f82d, 0x000ad3b81a0d72fe),
+    P64::new(0xae900e2d7c9a6f7b, 0x000acd52beced79e),
+    P64::new(0x1c08431bdd18be89, 0x000aca9755063254),
+    P64::new(0xb370a66d684fd83f, 0x000ac7dd4cafb12a),
+    P64::new(0xb4be33e18f93b279, 0x000ac354f80dca44),
+    P64::new(0x310c50872a7dd5e3, 0x000ac26d5c2b8ad2),
+    P64::new(0x447ab1281276697d, 0x000abde997dabd3d),
+    P64::new(0xc2f122216b2a6c21, 0x000ab883aa1100a0),
+    P64::new(0xab99c8b5ae1c3059, 0x000ab4ed637f5a0b),
+    P64::new(0xb78e17a2227d593b, 0x000ab074e9febf52),
+    P64::new(0xabf97d03f7269c5d, 0x000aaf90778c2039),
+    P64::new(0x867aefc9fdbfe7ff, 0x000aab1c7684f034),
+    P64::new(0xf7f7ad182e47d5b7, 0x000aa78f20ebbb3e),
+    P64::new(0x50dff95a9847721b, 0x000aa23f8dafd4cc),
+    P64::new(0xe4cb8a0e83cb6a35, 0x000a9dd69cad5934),
+    P64::new(0x8da72ecdf9247a1d, 0x000a935004a07302),
+    P64::new(0xc5b04bfc87f31d87, 0x000a9270690f3d14),
+    P64::new(0xe2dcf622ea2b00f3, 0x000a90b1a0aa5d30),
+    P64::new(0xb9ce9f2e4972f46b, 0x000a8d35c9d731e9),
+    P64::new(0x1ed785c911bf59f9, 0x000a8a9a6a51f16c),
+    P64::new(0x4ddb8a4eed70e085, 0x000a88de370f596b),
+    P64::new(0x81e93b4df68c24fd, 0x000a856786adae36),
+    P64::new(0xee0d0812afcd8357, 0x000a7da4c77d3161),
+    P64::new(0xf62e3ba72268a891, 0x000a7959f863d4a1),
+    P64::new(0x3194d367c8154147, 0x000a76c85e80c195),
+    P64::new(0xd096ede8e30c20d5, 0x000a743806dc44c4),
+    P64::new(0xd68624d27b87a77f, 0x000a735d866dfa0a),
+    P64::new(0xb728fcdc11c8204d, 0x000a70cedb02531e),
+    P64::new(0x9d6b6038077e066f, 0x000a6c8e842c770f),
+    P64::new(0xaa732d7a4a360d93, 0x000a67791215dd74),
+    P64::new(0x36af98a423972db5, 0x000a66a0a51d363d),
+    P64::new(0xc31d00da12940f17, 0x000a626893011861),
+    P64::new(0xed85352107410b25, 0x000a5fe22c55c089),
+    P64::new(0x829c85ee6db8567b, 0x000a5d5cffb77275),
+    P64::new(0xef60258952cc6d89, 0x000a5ad90c4186e5),
+    P64::new(0xcf28c2e0da787741, 0x000a578057e7c2eb),
+    P64::new(0x57567d8494af28f7, 0x000a54ff3bb10e91),
+    P64::new(0x2c7c98518f174031, 0x000a50d5683edc94),
+    P64::new(0xb28b363a36825ae7, 0x000a4e57854b3df4),
+    P64::new(0xed1ffeb64f9ae769, 0x000a4d8328c4b800),
+    P64::new(0xcbbb0115e9b9a31f, 0x000a4b06e01d97b3),
+    P64::new(0x8d3c5fecb7f9e4ed, 0x000a488bca2c4449),
+    P64::new(0x816271698195cfc3, 0x000a4611e6132ed5),
+    P64::new(0x9ac939d1c2b1d35d, 0x000a41f40f39e646),
+    P64::new(0xdd9fb7017b0ec455, 0x000a3eab5c3e44e9),
+    P64::new(0xc94cab1e57276e3d, 0x000a34ddd50561e0),
+    P64::new(0x8b8806b117c79913, 0x000a326d60e94186),
+    P64::new(0xa9e63292a3269fd1, 0x000a2985a81ce614),
+    P64::new(0x76da5710f1e989fb, 0x000a28b72e26f82e),
+    P64::new(0xdded6688d83a918d, 0x000a217aa3479693),
+    P64::new(0x4e446b6a305428f9, 0x000a1fe05c62df4b),
+    P64::new(0x4ddaca7a3696cfb1, 0x000a1cad538aebf9),
+    P64::new(0x7eadc4eb87f26ed3, 0x000a18b05f490083),
+    P64::new(0x76c13a0ff04c00c9, 0x000a0ccc4c28fc31),
+    P64::new(0xcbf800504d2a2681, 0x000a09a544d01ffe),
+    P64::new(0x0731dada6c4fec9b, 0x000a0294aa53e9a2),
+    P64::new(0xbcb52a664e63f627, 0x000a01041a6aaed5),
+    P64::new(0xf1f9abda071c2aa9, 0x000a003c01680870),
+    P64::new(0xf262ffa620ffe20b, 0x0009fc5558a971c8),
+    P64::new(0x93774a3d57199a99, 0x0009f9ff9c3c03e5),
+    P64::new(0xfb3541cd467a1903, 0x0009f9389b864ab9),
+    P64::new(0x6828cab6b4fe8f51, 0x0009f6e4534bdca8),
+    P64::new(0x12ac03e3d624cc9d, 0x0009f557687235c2),
+    P64::new(0x6363bd1e9bb7d7f7, 0x0009ee633c0391ab),
+    P64::new(0x334cfd676a484d2f, 0x0009eb4f28e0bb39),
+    P64::new(0xd511acd86f143a53, 0x0009e6b49e92e4bb),
+    P64::new(0x73fc2490e0062be5, 0x0009dfd4ccbd0045),
+    P64::new(0x10780dda36b78b55, 0x0009d9c0828536c1),
+    P64::new(0xabf601274064e0ab, 0x0009d77ad449f777),
+    P64::new(0x3ef3e4ca27e4a2cd, 0x0009d6b92b28ee48),
+    P64::new(0x9216a26e690a16f1, 0x0009d231a476ed51),
+    P64::new(0xbae4849e6034bda7, 0x0009cfef711bf120),
+    P64::new(0xf943a0520e01e9e1, 0x0009cc2e1448b765),
+    P64::new(0x7c89958f48f6658b, 0x0009cb6e26cbc64d),
+    P64::new(0xe67128750e0545a5, 0x0009c7b03b4a9c67),
+    P64::new(0xc6c9e1d414516ccf, 0x0009c6f0fd980ab1),
+    P64::new(0x805307f996e9e81d, 0x0009c4b3f3a30c3f),
+    P64::new(0x3eddd2cff46ad5bf, 0x0009c0fb29436687),
+    P64::new(0x35582c1aeb5aae85, 0x0009bbca025b7aec),
+    P64::new(0x4973c88573ef6eb1, 0x0009ba4f4421e52c),
+    P64::new(0x3063f627c1e715d9, 0x0009b1783809ff03),
+    P64::new(0x711ad679a8dcc243, 0x0009b0bc5b4d2eac),
+    P64::new(0x51c224a17a3db4b3, 0x0009aae172fd8b9c),
+    P64::new(0x612325ca50ddaed5, 0x0009aa26954607ed),
+    P64::new(0x9929a7b6b7958b37, 0x0009a681e758a022),
+    P64::new(0xa78d222e5a857bb9, 0x0009a5c7b284942e),
+    P64::new(0x3ad0ffe3198d139b, 0x0009a2264ecc5558),
+    P64::new(0x08b4659ac547ed17, 0x00099aebb39be56f),
+    P64::new(0x1752e8904aff1003, 0x0009997ae1a9faac),
+    P64::new(0x60745c37ee4e5925, 0x000998c2a22b6900),
+    P64::new(0x29e2da1f6557ee51, 0x000997527603f8a8),
+    P64::new(0x80d78c24ac49cb89, 0x00099473685e4d50),
+    P64::new(0xc56c3b495c8d1f79, 0x00098eba72512a13),
+    P64::new(0xcf5bdf9f5088ac2f, 0x00098c96d8dee9e1),
+    P64::new(0x8a44800e4fae4e7d, 0x00098a743453554e),
+    P64::new(0xdd76384277e578e7, 0x000989be33c9e6bd),
+    P64::new(0x20b1562d2703facb, 0x0009857c692e9a59),
+    P64::new(0xef56caf96e9d8e3b, 0x00097fd540c05c9e),
+    P64::new(0xf54061416aede033, 0x00097d04302ed944),
+    P64::new(0xe0bc78c21a26e4ff, 0x00097b9c48289935),
+    P64::new(0x0524f92731a179cd, 0x0009798133ece717),
+    P64::new(0x5d3b4ad7deafec8b, 0x00096f07c683689e),
+    P64::new(0x508828f744da88ad, 0x00096e55d6393fc5),
+    P64::new(0x6e82014031710bcf, 0x00096addad861696),
+    P64::new(0xadf3b77a22595dd1, 0x00096a2c5a2cf0cf),
+    P64::new(0x0d8f0c03f7ea8a87, 0x00096818fc825eba),
+    P64::new(0x2c49e3483c3a05f3, 0x000966b74027f48a),
+    P64::new(0xccecbc98c91274c1, 0x000964a56850b8ed),
+    P64::new(0x273a08941bb71e77, 0x000962947990eb36),
+    P64::new(0xdead5a1e3f341baf, 0x00095fd4a4c885e0),
+    P64::new(0x83eee092593309fd, 0x00095dc5d3954fde),
+    P64::new(0x4af5f1bd3ae87ce9, 0x00095c671ddfe516),
+    P64::new(0x4ca85ad2301c9e6d, 0x0009584d6340ddf1),
+    P64::new(0x1b19592cd31a3943, 0x00095641de84afcc),
+    P64::new(0x3e7aa05e6dcd81bb, 0x000953893c386521),
+    P64::new(0x86336cecb02ba47f, 0x00094f7740d87794),
+    P64::new(0xa96b30d0c8a44b2b, 0x00094e1cb70c9ce0),
+    P64::new(0xb7c63fa0cfca0571, 0x00094962ecbcc7ce),
+    P64::new(0x8eaf59b405a642b5, 0x00094559c69059cf),
+    P64::new(0xdf29e9cbb536dc17, 0x000941ff7e640716),
+    P64::new(0xed14132c82c1d43f, 0x000939fd7a24b099),
+    P64::new(0xaf68778e34caab0d, 0x000937ff22c014bd),
+    P64::new(0xa4f04a3368941d31, 0x000934050872c09e),
+    P64::new(0xe9960969357c07e7, 0x00093209446d56f6),
+    P64::new(0xeb47b62b7360b469, 0x0009316033b5bd22),
+    P64::new(0x64c653d779ae730f, 0x00092a22b9a79374),
+    P64::new(0x479702d3319915c7, 0x000927838edba206),
+    P64::new(0xef3c3eebc6803239, 0x000921a2e7112833),
+    P64::new(0x93807b1a2e3c0e1b, 0x00091e623d5660d0),
+    P64::new(0x8167e33e3f478029, 0x00091c6fc0cab8b6),
+    P64::new(0x60cb76e38c339397, 0x000917e7d88028eb),
+    P64::new(0xae34788ffe4bc283, 0x0009169d455585cd),
+    P64::new(0x4b6246a0c6c093a5, 0x000915f81ef2d529),
+    P64::new(0x872e594b12b03efb, 0x0009140938595d3a),
+    P64::new(0xbc0ae83ce9045b15, 0x000910d2360a450e),
+    P64::new(0x0ad30a3917e0968d, 0x00090e417104eabd),
+    P64::new(0x124ef5a4e1c7cd63, 0x00090c55d0fdea28),
+    P64::new(0x5b98fe0e9fe17aaf, 0x00090b0e84c04f20),
+    P64::new(0x414306cfe45400fd, 0x000909243fac6b70),
+    P64::new(0xa06d1b4fd391e8bb, 0x0008ff9d0440d137),
+    P64::new(0x11939803a60c2381, 0x0008fb3192789d73),
+    P64::new(0x668c11cc37ea6b23, 0x0008f80c0d5031e3),
+    P64::new(0x83f9b2089dc10645, 0x0008f76b3664f164),
+    P64::new(0x65dc8ae47af277a9, 0x0008f3a80550abc3),
+    P64::new(0x6e2368b9c685770b, 0x0008f087c50e00c4),
+    P64::new(0x3ea137aeba5a6b2d, 0x0008efe7fb408cc2),
+    P64::new(0x735f57adca48f19d, 0x0008eaecce5c4fd7),
+    P64::new(0x69a8de0ba1b18107, 0x0008ea4dccaaec0b),
+    P64::new(0x8fb84bdf5822bd79, 0x0008e4ba9fbc2ff0),
+    P64::new(0xb8fab3b748562721, 0x0008dd5688a3b7d6),
+    P64::new(0xa6c658ea10a65c3b, 0x0008d7d3821fd94f),
+    P64::new(0xe56381f33ab5e549, 0x0008d5feb03c31d7),
+    P64::new(0xe3c224da14988139, 0x0008d12033cc9d30),
+    P64::new(0x438c253e6d99f513, 0x0008cbac4dec6a82),
+    P64::new(0xc1b99f8841a3a6e1, 0x0008c9dc80ab604b),
+    P64::new(0x63fa18c79c54fa8b, 0x0008c942115dcc96),
+    P64::new(0xe7f6f609619d0d1d, 0x0008c3d7df67b539),
+    P64::new(0x7b39ef3b70afc109, 0x0008c2a4bc35cb3b),
+    P64::new(0x73922c61ca7452bf, 0x0008c0d8a4f1f264),
+    P64::new(0x28d96828332372c1, 0x0008c03f71cbf906),
+    P64::new(0x6b6e92968c4e8463, 0x0008bd42abd9a107),
+    P64::new(0x571861f084962edb, 0x0008bae051d7f6ff),
+    P64::new(0xd935c64f140f1ef5, 0x0008b7e735068135),
+    P64::new(0x96459f8fd72a4c4b, 0x0008b61f82c5fb08),
+    P64::new(0x410ba9a2a18242d9, 0x0008b4588a74a05a),
+    P64::new(0xcf90979f89870391, 0x0008b1fb0a7ed403),
+    P64::new(0x10f94ff26bc00add, 0x0008b0ccc5d8f5c8),
+    P64::new(0xa6619fbb9da139b3, 0x0008af07f8ac5146),
+    P64::new(0x765a23334efb03d5, 0x0008ae71328ffd49),
+    P64::new(0x6f2f613b5e631837, 0x0008ab8086624822),
+    P64::new(0x666b99bfbcd368b9, 0x0008aaea3ab5ae89),
+    P64::new(0x922b78eb01ed45bd, 0x0008a7661f7020fe),
+    P64::new(0x7079a199c31de6a9, 0x0008a63ab88aa8dd),
+    P64::new(0xa181abcda167be5f, 0x0008a47a35d020f3),
+    P64::new(0x2f6dbbcab3a9822d, 0x0008a2ba68a3cebf),
+    P64::new(0xc5a83ff0e43eba17, 0x0008a2254c852497),
+    P64::new(0x28c68613dda7d97b, 0x00089ea849898bb3),
+    P64::new(0x5cf33ed49efa5007, 0x00089d7f3e285109),
+    P64::new(0x9125fdead661590d, 0x000899720af36739),
+    P64::new(0xaee67f478c7325e7, 0x00089442160d11dc),
+    P64::new(0x735b1274a0e89653, 0x0008931bd5875a22),
+    P64::new(0x733b56eae1a4e621, 0x000891630877aedf),
+    P64::new(0x1944ffb316ffe65d, 0x00088baaad83e38f),
+    P64::new(0xf26bc3cfd2a01449, 0x00088a86b9090aa4),
+    P64::new(0xb5827ba68b83e201, 0x0008883fb99bf244),
+    P64::new(0xac139507e48eefb7, 0x0008868b45e727ee),
+    P64::new(0xeb7676b25834fda3, 0x00088568aef30d47),
+    P64::new(0xad898f4763da5c1b, 0x0008832468f0bcdd),
+    P64::new(0xea906f224398f9a7, 0x00088202b9a4df76),
+    P64::new(0xa8aff3caca28cdad, 0x00087e0f31872e9b),
+    P64::new(0x46c53aa36b19b083, 0x00087c5ecd731f42),
+    P64::new(0x9ada32b09603e8cf, 0x00087b3eea3bb388),
+    P64::new(0xd31f842ef5d8e915, 0x00087751a6c67d78),
+    P64::new(0x6124af44730a33f9, 0x000873f6e2f9d34a),
+    P64::new(0x828ec4c2b6e64a85, 0x000872d938dcfc01),
+    P64::new(0x3d6f49df999638af, 0x0008724a80151dba),
+    P64::new(0x7641460a0ea89b65, 0x000869f677f6cc1a),
+    P64::new(0x97703f98fb7fe291, 0x000868db701df58d),
+    P64::new(0xd343c209e3e6b7b9, 0x0008623f563a7d6d),
+    P64::new(0x4e5fc01f6a41406f, 0x00086099ef0c8886),
+    P64::new(0xb78a05b08aa4bcbd, 0x00085ef52d38fe87),
+    P64::new(0x3434a14919d34561, 0x00085bad981c7847),
+    P64::new(0xccead7dee120f525, 0x0008586893de7cfc),
+    P64::new(0xe1375a2bccd87673, 0x0008549b491e9efe),
+    P64::new(0xf727d51420a57141, 0x000852fb3859bea4),
+    P64::new(0x2c3b68cfbcebb00d, 0x000851e631fc08f8),
+    P64::new(0xda91e2f3e17542f7, 0x0008515bc9cde5f1),
+    P64::new(0xb55f6100ae95d6e3, 0x000850472f6185b3),
+    P64::new(0x6a0c608e0bbaa975, 0x00084b6defbc166b),
+    P64::new(0xac5f2fc151c016cb, 0x000849d17159854b),
+    P64::new(0xb1e5af8146e4d00f, 0x0008469a54a20645),
+    P64::new(0x6e283d3b112602c7, 0x00084476f9401ade),
+    P64::new(0xf9a48bcb76c96e55, 0x000842dd2e2dc25d),
+    P64::new(0xa776780ca4c0e101, 0x000841cc543f58cb),
+    P64::new(0x8d40a2d47d99c7c5, 0x00083e9b6c3df688),
+    P64::new(0x4ed9d8a7aedcefef, 0x00083e1382f22ff9),
+    P64::new(0x55c5cf9586072313, 0x00083ae57a327933),
+    P64::new(0x62c640e386ef1f09, 0x000832fd15e00939),
+    P64::new(0xdb876e7feb8b02f9, 0x00082ecb9c6669ac),
+    P64::new(0x5b85ac1558bdf263, 0x00082e45ba6652c4),
+    P64::new(0xb2b13930c2a889b1, 0x00082cb47b00abaa),
+    P64::new(0xdf53c897124f8c57, 0x000826fa5d0ce5aa),
+    P64::new(0x68a69390fdce78dd, 0x000823598cfc6865),
+    P64::new(0x5a1e8f0261e6e7b3, 0x000821cc79da73f1),
+    P64::new(0xcce38a9ccaab014d, 0x00081f37ff3d12c0),
+    P64::new(0xb0cd4811fe6a8171, 0x00081c21947b0acd),
+    P64::new(0x911c24573e445027, 0x00081a97404af5f7),
+    P64::new(0x9e86401e61cac4a9, 0x00081a13f02d110e),
+    P64::new(0xfd2731405f265eb5, 0x0008190d81c9877b),
+    P64::new(0x3f4c00205c05b02d, 0x000817016c0b3ffd),
+    P64::new(0xe92e3d0a829a974f, 0x00081473c50ac33e),
+    P64::new(0xdec216e5aa47169d, 0x000812ec59f2d11a),
+    P64::new(0xa0397bf3448bcd73, 0x0008116582e237c8),
+    P64::new(0x9ecf538d7efa905b, 0x00080b4fe85ec545),
+    P64::new(0xb1037b5f84886421, 0x000807c7894d029a),
 ];
 
 //////////////////// Tables for Miller-rabin bases of 32/64-bit integers using Bradley's hashing ////////////////////
diff --git a/src/traits.rs b/src/traits.rs
index 2ae6e18..6f0f4d4 100644
--- a/src/traits.rs
+++ b/src/traits.rs
@@ -110,7 +110,7 @@ impl Default for PrimalityTestConfig {
 }
 
 impl PrimalityTestConfig {
-    /// Create a configuration with the known stongest deterministic primality test
+    /// Create a configuration with the **stongest deterministic** primality test available
     pub fn strict() -> Self {
         Self::bpsw() // TODO: change to 2-base SPRP + VPRP
     }
@@ -204,11 +204,6 @@ pub trait ExactRoots: Roots + Pow<u32, Output = Self> + Clone {
     }
 }
 
-// TODO: implement quick div_exact (which might be useful in various functions)
-// REF: GMP `mpz_divexact`
-//      FLINT `fmpz_divexact`
-//      factor.c `divexact_21`
-
 // TODO: implement quick is_x_power (specifically is_235_power)
 // This could be used during factorization to filter out perfect powers
 // REF: PARI/GP `Z_ispowerall`, `is_357_power`