StochHMM  v0.34
Flexible Hidden Markov Model C++ Library and Application
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stochMath.h
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1 //
2 // stochMath.h
3 
4 //Copyright (c) 2007-2012 Paul C Lott
5 //University of California, Davis
6 //Genome and Biomedical Sciences Facility
7 //UC Davis Genome Center
8 //Ian Korf Lab
9 //Website: www.korflab.ucdavis.edu
10 //Email: lottpaul@gmail.com
11 //
12 //Permission is hereby granted, free of charge, to any person obtaining a copy of
13 //this software and associated documentation files (the "Software"), to deal in
14 //the Software without restriction, including without limitation the rights to
15 //use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
16 //the Software, and to permit persons to whom the Software is furnished to do so,
17 //subject to the following conditions:
18 //
19 //The above copyright notice and this permission notice shall be included in all
20 //copies or substantial portions of the Software.
21 //
22 //THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
23 //IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
24 //FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
25 //COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
26 //IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
27 //CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
28 #ifndef STOCHMATH_H
29 #define STOCHMATH_H
30 
31 #include <math.h>
32 #include <iostream>
33 #include <vector>
34 #include <limits>
35 #include <stdint.h>
36 #include <algorithm>
37 
38 #ifndef SIZE_MAX
39 #define SIZE_MAX ((size_t)-1)
40 #endif
41 
42 #ifndef UINT16_MAX
43 #define UINT16_MAX 65535
44 #endif
45 
46 
47 namespace StochHMM{
48 
49  #define PI 3.145926535897932
50 
51  //FIXME: Need to generate dynamically once upon initialization of HMM. System differences between (int,long,...);
52  //Or just leave it. It may work well enough;
53 
54 #if __LP64__
55  const uint64_t POWER[32][128] = {
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77  {1ULL, 2097152ULL, 10460353203ULL, 4398046511104ULL, 476837158203125ULL, 21936950640377856ULL, 558545864083284007ULL, 9223372036854775808ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL},
78  {1ULL, 4194304ULL, 31381059609ULL, 17592186044416ULL, 2384185791015625ULL, 131621703842267136ULL, 3909821048582988049ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL},
79  {1ULL, 8388608ULL, 94143178827ULL, 70368744177664ULL, 11920928955078125ULL, 789730223053602816ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL},
80  {1ULL, 16777216ULL, 282429536481ULL, 281474976710656ULL, 59604644775390625ULL, 4738381338321616896ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL},
81  {1ULL, 33554432ULL, 847288609443ULL, 1125899906842624ULL, 298023223876953125ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL},
82  {1ULL, 67108864ULL, 2541865828329ULL, 4503599627370496ULL, 1490116119384765625ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL},
83  {1ULL, 134217728ULL, 7625597484987ULL, 18014398509481984ULL, 7450580596923828125ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL},
84  {1ULL, 268435456ULL, 22876792454961ULL, 72057594037927936ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL},
85  {1ULL, 536870912ULL, 68630377364883ULL, 288230376151711744ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL},
86  {1ULL, 1073741824ULL, 205891132094649ULL, 1152921504606846976ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL},
87  {1ULL, 2147483648ULL, 617673396283947ULL, 4611686018427387904ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL, 0ULL}
88  };
89 #else
90 
91  const uint32_t POWER[32][128] = {
92  {1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL, 1UL},
93  {1UL, 2UL, 3UL, 4UL, 5UL, 6UL, 7UL, 8UL, 9UL, 10UL, 11UL, 12UL, 13UL, 14UL, 15UL, 16UL, 17UL, 18UL, 19UL, 20UL, 21UL, 22UL, 23UL, 24UL, 25UL, 26UL, 27UL, 28UL, 29UL, 30UL, 31UL, 32UL, 33UL, 34UL, 35UL, 36UL, 37UL, 38UL, 39UL, 40UL, 41UL, 42UL, 43UL, 44UL, 45UL, 46UL, 47UL, 48UL, 49UL, 50UL, 51UL, 52UL, 53UL, 54UL, 55UL, 56UL, 57UL, 58UL, 59UL, 60UL, 61UL, 62UL, 63UL, 64UL, 65UL, 66UL, 67UL, 68UL, 69UL, 70UL, 71UL, 72UL, 73UL, 74UL, 75UL, 76UL, 77UL, 78UL, 79UL, 80UL, 81UL, 82UL, 83UL, 84UL, 85UL, 86UL, 87UL, 88UL, 89UL, 90UL, 91UL, 92UL, 93UL, 94UL, 95UL, 96UL, 97UL, 98UL, 99UL, 100UL, 101UL, 102UL, 103UL, 104UL, 105UL, 106UL, 107UL, 108UL, 109UL, 110UL, 111UL, 112UL, 113UL, 114UL, 115UL, 116UL, 117UL, 118UL, 119UL, 120UL, 121UL, 122UL, 123UL, 124UL, 125UL, 126UL, 127UL, 128UL},
94  {1UL, 4UL, 9UL, 16UL, 25UL, 36UL, 49UL, 64UL, 81UL, 100UL, 121UL, 144UL, 169UL, 196UL, 225UL, 256UL, 289UL, 324UL, 361UL, 400UL, 441UL, 484UL, 529UL, 576UL, 625UL, 676UL, 729UL, 784UL, 841UL, 900UL, 961UL, 1024UL, 1089UL, 1156UL, 1225UL, 1296UL, 1369UL, 1444UL, 1521UL, 1600UL, 1681UL, 1764UL, 1849UL, 1936UL, 2025UL, 2116UL, 2209UL, 2304UL, 2401UL, 2500UL, 2601UL, 2704UL, 2809UL, 2916UL, 3025UL, 3136UL, 3249UL, 3364UL, 3481UL, 3600UL, 3721UL, 3844UL, 3969UL, 4096UL, 4225UL, 4356UL, 4489UL, 4624UL, 4761UL, 4900UL, 5041UL, 5184UL, 5329UL, 5476UL, 5625UL, 5776UL, 5929UL, 6084UL, 6241UL, 6400UL, 6561UL, 6724UL, 6889UL, 7056UL, 7225UL, 7396UL, 7569UL, 7744UL, 7921UL, 8100UL, 8281UL, 8464UL, 8649UL, 8836UL, 9025UL, 9216UL, 9409UL, 9604UL, 9801UL, 10000UL, 10201UL, 10404UL, 10609UL, 10816UL, 11025UL, 11236UL, 11449UL, 11664UL, 11881UL, 12100UL, 12321UL, 12544UL, 12769UL, 12996UL, 13225UL, 13456UL, 13689UL, 13924UL, 14161UL, 14400UL, 14641UL, 14884UL, 15129UL, 15376UL, 15625UL, 15876UL, 16129UL, 16384UL},
95  {1UL, 8UL, 27UL, 64UL, 125UL, 216UL, 343UL, 512UL, 729UL, 1000UL, 1331UL, 1728UL, 2197UL, 2744UL, 3375UL, 4096UL, 4913UL, 5832UL, 6859UL, 8000UL, 9261UL, 10648UL, 12167UL, 13824UL, 15625UL, 17576UL, 19683UL, 21952UL, 24389UL, 27000UL, 29791UL, 32768UL, 35937UL, 39304UL, 42875UL, 46656UL, 50653UL, 54872UL, 59319UL, 64000UL, 68921UL, 74088UL, 79507UL, 85184UL, 91125UL, 97336UL, 103823UL, 110592UL, 117649UL, 125000UL, 132651UL, 140608UL, 148877UL, 157464UL, 166375UL, 175616UL, 185193UL, 195112UL, 205379UL, 216000UL, 226981UL, 238328UL, 250047UL, 262144UL, 274625UL, 287496UL, 300763UL, 314432UL, 328509UL, 343000UL, 357911UL, 373248UL, 389017UL, 405224UL, 421875UL, 438976UL, 456533UL, 474552UL, 493039UL, 512000UL, 531441UL, 551368UL, 571787UL, 592704UL, 614125UL, 636056UL, 658503UL, 681472UL, 704969UL, 729000UL, 753571UL, 778688UL, 804357UL, 830584UL, 857375UL, 884736UL, 912673UL, 941192UL, 970299UL, 1000000UL, 1030301UL, 1061208UL, 1092727UL, 1124864UL, 1157625UL, 1191016UL, 1225043UL, 1259712UL, 1295029UL, 1331000UL, 1367631UL, 1404928UL, 1442897UL, 1481544UL, 1520875UL, 1560896UL, 1601613UL, 1643032UL, 1685159UL, 1728000UL, 1771561UL, 1815848UL, 1860867UL, 1906624UL, 1953125UL, 2000376UL, 2048383UL, 2097152UL},
96  {1UL, 16UL, 81UL, 256UL, 625UL, 1296UL, 2401UL, 4096UL, 6561UL, 10000UL, 14641UL, 20736UL, 28561UL, 38416UL, 50625UL, 65536UL, 83521UL, 104976UL, 130321UL, 160000UL, 194481UL, 234256UL, 279841UL, 331776UL, 390625UL, 456976UL, 531441UL, 614656UL, 707281UL, 810000UL, 923521UL, 1048576UL, 1185921UL, 1336336UL, 1500625UL, 1679616UL, 1874161UL, 2085136UL, 2313441UL, 2560000UL, 2825761UL, 3111696UL, 3418801UL, 3748096UL, 4100625UL, 4477456UL, 4879681UL, 5308416UL, 5764801UL, 6250000UL, 6765201UL, 7311616UL, 7890481UL, 8503056UL, 9150625UL, 9834496UL, 10556001UL, 11316496UL, 12117361UL, 12960000UL, 13845841UL, 14776336UL, 15752961UL, 16777216UL, 17850625UL, 18974736UL, 20151121UL, 21381376UL, 22667121UL, 24010000UL, 25411681UL, 26873856UL, 28398241UL, 29986576UL, 31640625UL, 33362176UL, 35153041UL, 37015056UL, 38950081UL, 40960000UL, 43046721UL, 45212176UL, 47458321UL, 49787136UL, 52200625UL, 54700816UL, 57289761UL, 59969536UL, 62742241UL, 65610000UL, 68574961UL, 71639296UL, 74805201UL, 78074896UL, 81450625UL, 84934656UL, 88529281UL, 92236816UL, 96059601UL, 100000000UL, 104060401UL, 108243216UL, 112550881UL, 116985856UL, 121550625UL, 126247696UL, 131079601UL, 136048896UL, 141158161UL, 146410000UL, 151807041UL, 157351936UL, 163047361UL, 168896016UL, 174900625UL, 181063936UL, 187388721UL, 193877776UL, 200533921UL, 207360000UL, 214358881UL, 221533456UL, 228886641UL, 236421376UL, 244140625UL, 252047376UL, 260144641UL, 268435456UL},
97  {1UL, 32UL, 243UL, 1024UL, 3125UL, 7776UL, 16807UL, 32768UL, 59049UL, 100000UL, 161051UL, 248832UL, 371293UL, 537824UL, 759375UL, 1048576UL, 1419857UL, 1889568UL, 2476099UL, 3200000UL, 4084101UL, 5153632UL, 6436343UL, 7962624UL, 9765625UL, 11881376UL, 14348907UL, 17210368UL, 20511149UL, 24300000UL, 28629151UL, 33554432UL, 39135393UL, 45435424UL, 52521875UL, 60466176UL, 69343957UL, 79235168UL, 90224199UL, 102400000UL, 115856201UL, 130691232UL, 147008443UL, 164916224UL, 184528125UL, 205962976UL, 229345007UL, 254803968UL, 282475249UL, 312500000UL, 345025251UL, 380204032UL, 418195493UL, 459165024UL, 503284375UL, 550731776UL, 601692057UL, 656356768UL, 714924299UL, 777600000UL, 844596301UL, 916132832UL, 992436543UL, 1073741824UL, 1160290625UL, 1252332576UL, 1350125107UL, 1453933568UL, 1564031349UL, 1680700000UL, 1804229351UL, 1934917632UL, 2073071593UL, 2219006624UL, 2373046875UL, 2535525376UL, 2706784157UL, 2887174368UL, 3077056399UL, 3276800000UL, 3486784401UL, 3707398432UL, 3939040643UL, 4182119424UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
98  {1UL, 64UL, 729UL, 4096UL, 15625UL, 46656UL, 117649UL, 262144UL, 531441UL, 1000000UL, 1771561UL, 2985984UL, 4826809UL, 7529536UL, 11390625UL, 16777216UL, 24137569UL, 34012224UL, 47045881UL, 64000000UL, 85766121UL, 113379904UL, 148035889UL, 191102976UL, 244140625UL, 308915776UL, 387420489UL, 481890304UL, 594823321UL, 729000000UL, 887503681UL, 1073741824UL, 1291467969UL, 1544804416UL, 1838265625UL, 2176782336UL, 2565726409UL, 3010936384UL, 3518743761UL, 4096000000UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
99  {1UL, 128UL, 2187UL, 16384UL, 78125UL, 279936UL, 823543UL, 2097152UL, 4782969UL, 10000000UL, 19487171UL, 35831808UL, 62748517UL, 105413504UL, 170859375UL, 268435456UL, 410338673UL, 612220032UL, 893871739UL, 1280000000UL, 1801088541UL, 2494357888UL, 3404825447UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
100  {1UL, 256UL, 6561UL, 65536UL, 390625UL, 1679616UL, 5764801UL, 16777216UL, 43046721UL, 100000000UL, 214358881UL, 429981696UL, 815730721UL, 1475789056UL, 2562890625UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
101  {1UL, 512UL, 19683UL, 262144UL, 1953125UL, 10077696UL, 40353607UL, 134217728UL, 387420489UL, 1000000000UL, 2357947691UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
102  {1UL, 1024UL, 59049UL, 1048576UL, 9765625UL, 60466176UL, 282475249UL, 1073741824UL, 3486784401UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
103  {1UL, 2048UL, 177147UL, 4194304UL, 48828125UL, 362797056UL, 1977326743UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
104  {1UL, 4096UL, 531441UL, 16777216UL, 244140625UL, 2176782336UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
105  {1UL, 8192UL, 1594323UL, 67108864UL, 1220703125UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
106  {1UL, 16384UL, 4782969UL, 268435456UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
107  {1UL, 32768UL, 14348907UL, 1073741824UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
108  {1UL, 65536UL, 43046721UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
109  {1UL, 131072UL, 129140163UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
110  {1UL, 262144UL, 387420489UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
111  {1UL, 524288UL, 1162261467UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
112  {1UL, 1048576UL, 3486784401UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
113  {1UL, 2097152UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
114  {1UL, 4194304UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
115  {1UL, 8388608UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
116  {1UL, 16777216UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
117  {1UL, 33554432UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
118  {1UL, 67108864UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
119  {1UL, 134217728UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
120  {1UL, 268435456UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
121  {1UL, 536870912UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
122  {1UL, 1073741824UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
123  {1UL, 2147483648UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL, 0UL},
124  };
125 #endif
126 
127 
128  //! Integer Power function
129  //! The function is overflow safe, all the calculations are checked to make sure that the result won't overflow. Works for positive or negative bases.
130  //! Any overflow will result in the return value of zero
131  //! \param base
132  //! \param exponent
133  //! \return zero if underflow or overflow occurs.
134  template <typename T>
135  T integerPower(T base, T exponent){
136  bool negative(false);
137  T max = std::numeric_limits<T>::max();
138  if (base<1){
139  base=abs(base);
140  if (exponent%2!=0){
141  negative=true;
142  }
143  }
144 
145  T result = 1;
146  while (exponent)
147  {
148  if (exponent & 1){
149  if (result > max/base){ //Determine if value of result*base > INT_MAX;
150  return 0;
151  }
152 
153  result *= base;
154  }
155 
156  exponent >>= 1;
157 
158  if (exponent != 0){
159  if (base > max/base){ //Determine if value of base*base > INT_MAX;
160  return 0;
161  }
162  base *= base;
163  }
164  }
165 
166  if (negative){
167  return (-1*result);
168  }
169  return (result);
170 
171  };
172 
173 
174  //! Takes two logd values and adds them together
175  //! \param first log'd Double value
176  //! \param second log'd Double value
177  //! \return Log'd sum of two values
178  template<typename T>
179  T addLog(T first, T second){
180  if (first==-INFINITY){
181  return second;
182  }
183  else if (second==-INFINITY){
184  return first;
185  }
186  else if (first>second){
187  return first+log(1+exp(second-first));
188  }
189  else{
190  return second+log(1+exp(first-second));
191  }
192  }
193 
194 
195  /*! \fn void addVectorCombinatorial(std::vector< REAL >& result, std::vector< REAL >& lhs, std::vector< REAL >& rhs)
196  \brief Adds the lhs and rhs vector combinatorially in result
197  \param lhs vector of (ints or doubles)
198  \param rhs vector of (ints or doubles)
199  \param results Result of the two vectors added together
200 
201  ----------------------------------------------------------------------------
202  Description: addVectorCombinatorial
203  Adds the values of vectors combinatorial
204  Example [ 1 4 ] + [ 2 7 ] = [ 2 6 8 11 ]
205  ----------------------------------------------------------------------------
206 
207  */
208  template<typename T>
209  void addVectorCombinatorial(std::vector<T>& result, std::vector<T>& lhs, std::vector<T>& rhs){
210 
211  if (result.size()>0){
212  result.clear();
213  }
214 
215  //If either vector is empty then return copy of the other
216  if (lhs.size()==0){
217  result.assign(rhs.begin(),rhs.end());
218  return;
219  }
220  else if (rhs.size()==0){
221  result.assign(lhs.begin(),lhs.end());
222  return;
223  }
224 
225  for(size_t i=0;i<lhs.size();i++){
226  for(size_t j=0;j<rhs.size();j++){
227  result.push_back(lhs[i]+rhs[j]);
228  }
229  }
230  return;
231  }
232 
233 
234  /*! \fn void multiplyVectorCombinatorial(std::vector< REAL >& result, std::vector< REAL >& lhs, std::vector< REAL >& rhs)
235  \brief Multiply teh lhs and rhs vector combinatorially in result
236  \param lhs vector of (ints or doubles)
237  \param rhs vector of (ints or doubles)
238  \param results Result of the two vectors added together
239  */
240  template<typename T>
241  void multiplyVectorCombinatorial(std::vector<T>& result, std::vector<T>& lhs, std::vector<T>& rhs){
242  if (result.size()>0){
243  result.clear();
244  }
245 
246  //If either vector is empty then return copy of the other
247  if (lhs.size()==0){
248  result.assign(rhs.begin(),rhs.end());
249  return;
250  }
251  else if (rhs.size()==0){
252  result.assign(lhs.begin(),lhs.end());
253  return;
254  }
255 
256 
257  for(size_t i=0;i<lhs.size();i++){
258  for(size_t j=0;j<rhs.size();j++){
259  result.push_back(lhs[i]*rhs[j]);
260  }
261  }
262  return;
263  }
264 
265 
266  /*! \fn void addToVector(std::vector<REAL>& vec ,REAL value)
267  \brief Adds value to each indices of the vector
268  \param vec Reference to vector
269  \param value Value to add to vector
270  */
271  template<typename T>
272  void addValueToVector(std::vector<T>& vec,T value){
273  for(size_t i=0;i<vec.size();i++){
274  vec[i]+=value;
275  }
276  return;
277  }
278 
279 
280  /*! \fn void multiplyValueToVector(std::vector<REAL>& vec, REAL value)
281  \brief Multiply value to each indices of the vector
282  \param vec Reference to vector
283  \param value Value to multiply each indices by
284  */
285  template<typename T>
286  void multiplyValueToVector(std::vector<T>& vec, T value){
287  for(size_t i=0;i<vec.size();i++){
288  vec[i]*=value;
289  }
290  return;
291  }
292 
293 
294  /*! \fn void divideValueToVector(std::vector<REAL>& vec, REAL value)
295  \brief Divide value to each indices of the vector
296  \param vec Reference to vector
297  \param value Value to divide each indices by
298  */
299  template<typename T>
300  void divideValueToVector(std::vector<T>& vec,T value){
301  for(size_t i=0;i<vec.size();i++){
302  vec[i]/=value;
303  }
304  return;
305  }
306 
307 
308  //
309  void generateUnknownIndices(std::vector<size_t>&,size_t,size_t,size_t);
310 
311 
312  /*! \fn T sumVector(std::vector<T>& data)
313  \brief Sum the vector and return the sum
314  \param data Vector of doubles
315  */
316  template<class T>
317  T sumVector(std::vector<T>& data){
318  double sum=0;
319  for(size_t i=0;i<data.size();i++){
320  sum+=data[i];
321  }
322  return sum;
323  }
324 
325  /*! \fn T sumVector(std::vector<T>& data)
326  \brief Sum the vector and return the sum
327  \param data Vector of doubles
328  */
329  template<class T>
330  T sumVector(const std::vector<T>& data){
331  double sum=0;
332  for(size_t i=0;i<data.size();i++){
333  sum+=data[i];
334  }
335  return sum;
336  }
337 
338  /*! \fn T productVector(std::vector<T>& data)
339  \brief Multiply terms in vector and return the product
340  \param data Vector of T
341  */
342  template<class T>
343  T productVector(std::vector<T>& data){
344  double product=data[0];
345  for(size_t i=1;i<data.size();++i){
346  product*=data[i];
347  }
348  return product;
349  }
350 
351 
352  /*! \fn double minVector(std::vector<double>& data)
353  \brief Get Minimum of the vector
354  \param data Vector of doubles
355  */
356  template<typename T>
357  T minVector(std::vector<T>& data){
358  return *min_element(data.begin(), data.end());
359  }
360 
361  /*! \fn double maxVector(std::vector<doubles>& data)
362  \brief Get the Maximum of the vector
363  \param data Vector of doubles
364  */
365  template<typename T>
366  T maxVector(std::vector<T>& data){
367  return *max_element(data.begin(), data.end());
368  }
369 
370  /*! \fn T avgVector(std::vector<double>& data)
371  \brief Get the average of the vector
372  \param data Vector of doubles
373  */
374  template<typename T>
375  T avgVector(std::vector<T>& data){
376  return sumVector(data) / T(data.size());
377  }
378 
379 
380  /*! \fn void logVector(std::vector<double>& data)
381  \brief Take log of each element in vector
382  \param data Vector of doubles
383  */
384  template<typename T>
385  void logVector(std::vector<T>& data){
386  for(size_t i=0;i<data.size();i++){
387  data[i]=log(data[i]);
388  }
389  return;
390  }
391 
392  /*! \fn void expVector(std::vector<doubles>& data)
393  \brief Take the exponent of each element in the vector
394  \param data Vector of doubles
395  */
396  template<typename T>
397  void expVector(std::vector<T>& data){
398  for(size_t i=0;i<data.size();i++){
399  data[i]=exp(data[i]);
400  }
401  return;
402  }
403 
404  /*! \fn T avgLogVector(std::vector<double>& data)
405  \brief Get the average of the vector of log'd values
406  \param data Vector of doubles
407  */
408  template<typename T>
409  T avgLogVector(std::vector<T>& data){
410  expVector(data);
411  return log(sumVector(data) / T(data.size()));
412  }
413 
414 
415  /*! \fn void probVector(std::vector<double>& data)
416  \brief Convert the vector to probilities. Divide each indice by the sum of the vector
417  \param data Vecor of doubles
418  */
419  template<typename T>
420  void probVector(std::vector<T>& data){
421  T sum=sumVector(data);
422  for(size_t iter=0;iter<data.size();iter++){
423  if (sum==0){
424  data[iter]=0;
425  }
426  else{
427  data[iter]/=sum;
428  }
429  }
430  return;
431  }
432 
433  template <typename T>
434  void addVector(std::vector<T>& lhs, std::vector<T>& rhs){
435  transform(lhs.begin(), lhs.end(), rhs.begin(), lhs.begin(), std::plus<T>());
436  return;
437  }
438 
439  /*! \fn void logProbVector(std::vector<double>& data)
440  \brief Convert the vector to log of probilities. Divide each indice by the sum of the vector
441  \param data Vecor of doubles
442  */
443  template<typename T>
444  void logProbVector(std::vector<T>& data){
445  T sum=sumVector(data);
446  for(size_t iter=0;iter<data.size();iter++){
447  if (sum==0){
448  data[iter]=-INFINITY;
449  }
450  else{
451  data[iter] = log(data[iter]/sum);
452  }
453  }
454  return;
455  }
456 
457 
458  //Linear interpolation and extrapolation
459  /*! \fn double interpolate(std::pair<double,double>& a, std::pair<double,double>& b, double& cx)
460  \brief Interpolates the y value given cx and two surrounding points on either side a and b
461  \param a pair of doubles (X1,Y1)
462  \param b pair of doubles (X2,Y2)
463  \param cx double value X
464  */
465  double interpolate(std::pair<double,double>&,std::pair<double,double>&,double&);
466 
467 
468  /*! \fn double extrapolate(std::pair<double,double>& a, std::pair<double,double>& b, double& cx)
469  \brief Extrapolates the Y value of point given by cx and two previous points.
470  \param a pair of doubles (X1,Y1)
471  \param b pair of doubles (X2,Y2)
472  \param cx double value of X
473  */
474  double extrapolate(std::pair<double,double>&,std::pair<double,double>&,double&);
475 
476 
477  template <class T>
478  T min(std::vector<T> &set){
479  T min =set[0];
480  for(long i=set.size()-1;i>0;i--){
481  if (set[i]<min){ min=set[i];}
482  }
483  return min;
484  }
485 
486  template <class T>
487  T max(std::vector<T> &set){
488  T max=set[0];
489  for(long i=set.size()-1;i>0;i--){
490  if (set[i]>max){ max=set[i];}
491  }
492  return min;
493  }
494 
495  template <class T>
496  T construct_histogram (std::vector<T> &set,int N_bins){
497  T mini=min(set);
498  T maxi=max(set);
499  T delta=(maxi-mini+1)/N_bins;
500  std::vector<T> bin (N_bins,0);
501  for(size_t i=set.size()-1;i != SIZE_MAX;i--){
502  T value=floor((set[i]-mini)/delta);
503  bin(value)=bin(value)+1/(set.size()*delta);
504  }
505  return bin;
506  }
507 
508  template <class T>
509  T smooth_histogram (std::vector<T> histo, int intervals, int window_size, int iterations){
510  std::vector<T> s_histo=histo;
511  for (int i=1;i<=iterations;i++){
512  for (int b=0;b<=intervals-window_size;b++){
513  int c=b+floor((window_size-1)/2);
514  s_histo[c]=0;
515  for (int j=b;j<=b+window_size-1;i++){
516  s_histo[c]=s_histo[c]+histo[j]/window_size;
517  }
518  }
519  for (int b=0;b<=((window_size-1)/2)-1;b++){
520  s_histo=s_histo[floor((window_size-1)/2)];
521  }
522  for (int b=intervals-window_size+1+floor((window_size-1)/2); b<=intervals-1;i++){
523  s_histo[b]=s_histo[intervals-window_size+floor((window_size-1) / 2)];
524  }
525  histo=s_histo;
526  }
527  T sum=0;
528  for (int b=0;b<=intervals-1;b++){
529  sum+=sum+s_histo[b];
530  }
531  for (int b=0;b<=intervals-1;b++){
532  s_histo[b]/=sum;
533  }
534  return s_histo;
535  }
536 
537  //!Shannon's Entropy in log(2) space
538  float entropy(std::vector<float>& set);
539  double entropy(std::vector<double>& set);
540 
541  //!Shannon's Relative entropy (Kullback-Leibler Divergence)
542  //!Normalized for A->B and B->A
543  float rel_entropy(std::vector<float> &set, std::vector<float> &set2);
544  double rel_entropy(std::vector<double> &set, std::vector<double> &set2);
545 
546  double _integrate(double (*funct)(double, std::vector<double>&),double, double, std::vector<double>& );
547  double integrate(double (*funct)(double, std::vector<double>&),double, double, std::vector<double>&, double, double);
548 
549  double simpson(double (*funct)(double, std::vector<double>&),double alpha, double beta,double lower, double upper);
550  double adapt_simpson(double (*funct)(double, double, double),double alpha, double beta, double lower, double upper, double max_error, double sum);
551  double summation(double(*funct)(int,std::vector<double>&), int, int, std::vector<double>&);
552 
553  ////Functions
554 
555  //Incomplete gamma functions
556  double igamma_upper (double, double);
557  double igamma_lower (double, double);
558  double _igamma_lower (double, std::vector<double>&);
559  //Regularized gamma functions
560  double rgammap(double, double);
561  double rgammaq(double, double);
562 
563  //Beta Functions
564  double beta(double a, double b);
565 
566  //Incomplete Beta function
567  double ibeta(double,double,double);
568  float betaPDF(float x, float a, float b);
569  double _ibeta(double, std::vector<double>&);
570 
571  //Regularized Incomplete Beta function
572  double ribeta(double,double,double);
573 
574  double factorial(double);
575  double bin_coef (double, double);
576  int bin_coef(int,int);
577 
578  //!Logit function
579  //!Inverse of the sigmoidal logistic function
580  //!Also known as log-odds score or ratio
581  inline double logit(double x){
582  return log(x/(1-x));
583  }
584 
585 }
586 #endif
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