/* * Sobol sequence direction vectors. * * This file contains code to create direction vectors for generating sobol * sequences in high dimensions. It is adapted from code on this webpage: * * http://web.maths.unsw.edu.au/~fkuo/sobol/ * * From these papers: * * S. Joe and F. Y. Kuo, Remark on Algorithm 659: Implementing Sobol's quasirandom * sequence generator, ACM Trans. Math. Softw. 29, 49-57 (2003) * * S. Joe and F. Y. Kuo, Constructing Sobol sequences with better two-dimensional * projections, SIAM J. Sci. Comput. 30, 2635-2654 (2008) * */ /* Copyright (c) 2008, Frances Y. Kuo and Stephen Joe * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are met: * * * Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * * Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * * Neither the names of the copyright holders nor the names of the * University of New South Wales and the University of Waikato * and its contributors may be used to endorse or promote products derived * from this software without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ #include "util_debug.h" #include "util_types.h" #include "sobol.h" CCL_NAMESPACE_BEGIN #define SOBOL_MAX_NUMBER 32 typedef struct SobolDirectionNumbers { uint d, s, a; uint m[SOBOL_MAX_NUMBER]; } SobolDirectionNumbers; static SobolDirectionNumbers SOBOL_NUMBERS[SOBOL_MAX_DIMENSIONS-1] = { {2, 1, 0, {1}}, {3, 2, 1, {1, 3}}, {4, 3, 1, {1, 3, 1}}, {5, 3, 2, {1, 1, 1}}, {6, 4, 1, {1, 1, 3, 3}}, {7, 4, 4, {1, 3, 5, 13}}, {8, 5, 2, {1, 1, 5, 5, 17}}, {9, 5, 4, {1, 1, 5, 5, 5}}, {10, 5, 7, {1, 1, 7, 11, 19}}, {11, 5, 11, {1, 1, 5, 1, 1}}, {12, 5, 13, {1, 1, 1, 3, 11}}, {13, 5, 14, {1, 3, 5, 5, 31}}, {14, 6, 1, {1, 3, 3, 9, 7, 49}}, {15, 6, 13, {1, 1, 1, 15, 21, 21}}, {16, 6, 16, {1, 3, 1, 13, 27, 49}}, {17, 6, 19, {1, 1, 1, 15, 7, 5}}, {18, 6, 22, {1, 3, 1, 15, 13, 25}}, {19, 6, 25, {1, 1, 5, 5, 19, 61}}, {20, 7, 1, {1, 3, 7, 11, 23, 15, 103}}, {21, 7, 4, {1, 3, 7, 13, 13, 15, 69}}, {22, 7, 7, {1, 1, 3, 13, 7, 35, 63}}, {23, 7, 8, {1, 3, 5, 9, 1, 25, 53}}, {24, 7, 14, {1, 3, 1, 13, 9, 35, 107}}, {25, 7, 19, {1, 3, 1, 5, 27, 61, 31}}, {26, 7, 21, {1, 1, 5, 11, 19, 41, 61}}, {27, 7, 28, {1, 3, 5, 3, 3, 13, 69}}, {28, 7, 31, {1, 1, 7, 13, 1, 19, 1}}, {29, 7, 32, {1, 3, 7, 5, 13, 19, 59}}, {30, 7, 37, {1, 1, 3, 9, 25, 29, 41}}, {31, 7, 41, {1, 3, 5, 13, 23, 1, 55}}, {32, 7, 42, {1, 3, 7, 3, 13, 59, 17}}, {33, 7, 50, {1, 3, 1, 3, 5, 53, 69}}, {34, 7, 55, {1, 1, 5, 5, 23, 33, 13}}, {35, 7, 56, {1, 1, 7, 7, 1, 61, 123}}, {36, 7, 59, {1, 1, 7, 9, 13, 61, 49}}, {37, 7, 62, {1, 3, 3, 5, 3, 55, 33}}, {38, 8, 14, {1, 3, 1, 15, 31, 13, 49, 245}}, {39, 8, 21, {1, 3, 5, 15, 31, 59, 63, 97}}, {40, 8, 22, {1, 3, 1, 11, 11, 11, 77, 249}}, {41, 8, 38, {1, 3, 1, 11, 27, 43, 71, 9}}, {42, 8, 47, {1, 1, 7, 15, 21, 11, 81, 45}}, {43, 8, 49, {1, 3, 7, 3, 25, 31, 65, 79}}, {44, 8, 50, {1, 3, 1, 1, 19, 11, 3, 205}}, {45, 8, 52, {1, 1, 5, 9, 19, 21, 29, 157}}, {46, 8, 56, {1, 3, 7, 11, 1, 33, 89, 185}}, {47, 8, 67, {1, 3, 3, 3, 15, 9, 79, 71}}, {48, 8, 70, {1, 3, 7, 11, 15, 39, 119, 27}}, {49, 8, 84, {1, 1, 3, 1, 11, 31, 97, 225}}, {50, 8, 97, {1, 1, 1, 3, 23, 43, 57, 177}}, {51, 8, 103, {1, 3, 7, 7, 17, 17, 37, 71}}, {52, 8, 115, {1, 3, 1, 5, 27, 63, 123, 213}}, {53, 8, 122, {1, 1, 3, 5, 11, 43, 53, 133}}, {54, 9, 8, {1, 3, 5, 5, 29, 17, 47, 173, 479}}, {55, 9, 13, {1, 3, 3, 11, 3, 1, 109, 9, 69}}, {56, 9, 16, {1, 1, 1, 5, 17, 39, 23, 5, 343}}, {57, 9, 22, {1, 3, 1, 5, 25, 15, 31, 103, 499}}, {58, 9, 25, {1, 1, 1, 11, 11, 17, 63, 105, 183}}, {59, 9, 44, {1, 1, 5, 11, 9, 29, 97, 231, 363}}, {60, 9, 47, {1, 1, 5, 15, 19, 45, 41, 7, 383}}, {61, 9, 52, {1, 3, 7, 7, 31, 19, 83, 137, 221}}, {62, 9, 55, {1, 1, 1, 3, 23, 15, 111, 223, 83}}, {63, 9, 59, {1, 1, 5, 13, 31, 15, 55, 25, 161}}, {64, 9, 62, {1, 1, 3, 13, 25, 47, 39, 87, 257}}, {65, 9, 67, {1, 1, 1, 11, 21, 53, 125, 249, 293}}, {66, 9, 74, {1, 1, 7, 11, 11, 7, 57, 79, 323}}, {67, 9, 81, {1, 1, 5, 5, 17, 13, 81, 3, 131}}, {68, 9, 82, {1, 1, 7, 13, 23, 7, 65, 251, 475}}, {69, 9, 87, {1, 3, 5, 1, 9, 43, 3, 149, 11}}, {70, 9, 91, {1, 1, 3, 13, 31, 13, 13, 255, 487}}, {71, 9, 94, {1, 3, 3, 1, 5, 63, 89, 91, 127}}, {72, 9, 103, {1, 1, 3, 3, 1, 19, 123, 127, 237}}, {73, 9, 104, {1, 1, 5, 7, 23, 31, 37, 243, 289}}, {74, 9, 109, {1, 1, 5, 11, 17, 53, 117, 183, 491}}, {75, 9, 122, {1, 1, 1, 5, 1, 13, 13, 209, 345}}, {76, 9, 124, {1, 1, 3, 15, 1, 57, 115, 7, 33}}, {77, 9, 137, {1, 3, 1, 11, 7, 43, 81, 207, 175}}, {78, 9, 138, {1, 3, 1, 1, 15, 27, 63, 255, 49}}, {79, 9, 143, {1, 3, 5, 3, 27, 61, 105, 171, 305}}, {80, 9, 145, {1, 1, 5, 3, 1, 3, 57, 249, 149}}, {81, 9, 152, {1, 1, 3, 5, 5, 57, 15, 13, 159}}, {82, 9, 157, {1, 1, 1, 11, 7, 11, 105, 141, 225}}, {83, 9, 167, {1, 3, 3, 5, 27, 59, 121, 101, 271}}, {84, 9, 173, {1, 3, 5, 9, 11, 49, 51, 59, 115}}, {85, 9, 176, {1, 1, 7, 1, 23, 45, 125, 71, 419}}, {86, 9, 181, {1, 1, 3, 5, 23, 5, 105, 109, 75}}, {87, 9, 182, {1, 1, 7, 15, 7, 11, 67, 121, 453}}, {88, 9, 185, {1, 3, 7, 3, 9, 13, 31, 27, 449}}, {89, 9, 191, {1, 3, 1, 15, 19, 39, 39, 89, 15}}, {90, 9, 194, {1, 1, 1, 1, 1, 33, 73, 145, 379}}, {91, 9, 199, {1, 3, 1, 15, 15, 43, 29, 13, 483}}, {92, 9, 218, {1, 1, 7, 3, 19, 27, 85, 131, 431}}, {93, 9, 220, {1, 3, 3, 3, 5, 35, 23, 195, 349}}, {94, 9, 227, {1, 3, 3, 7, 9, 27, 39, 59, 297}}, {95, 9, 229, {1, 1, 3, 9, 11, 17, 13, 241, 157}}, {96, 9, 230, {1, 3, 7, 15, 25, 57, 33, 189, 213}}, {97, 9, 234, {1, 1, 7, 1, 9, 55, 73, 83, 217}}, {98, 9, 236, {1, 3, 3, 13, 19, 27, 23, 113, 249}}, {99, 9, 241, {1, 3, 5, 3, 23, 43, 3, 253, 479}}, {100, 9, 244, {1, 1, 5, 5, 11, 5, 45, 117, 217}}, {101, 9, 253, {1, 3, 3, 7, 29, 37, 33, 123, 147}}, {102, 10, 4, {1, 3, 1, 15, 5, 5, 37, 227, 223, 459}}, {103, 10, 13, {1, 1, 7, 5, 5, 39, 63, 255, 135, 487}}, {104, 10, 19, {1, 3, 1, 7, 9, 7, 87, 249, 217, 599}}, {105, 10, 22, {1, 1, 3, 13, 9, 47, 7, 225, 363, 247}}, {106, 10, 50, {1, 3, 7, 13, 19, 13, 9, 67, 9, 737}}, {107, 10, 55, {1, 3, 5, 5, 19, 59, 7, 41, 319, 677}}, {108, 10, 64, {1, 1, 5, 3, 31, 63, 15, 43, 207, 789}}, {109, 10, 69, {1, 1, 7, 9, 13, 39, 3, 47, 497, 169}}, {110, 10, 98, {1, 3, 1, 7, 21, 17, 97, 19, 415, 905}}, {111, 10, 107, {1, 3, 7, 1, 3, 31, 71, 111, 165, 127}}, {112, 10, 115, {1, 1, 5, 11, 1, 61, 83, 119, 203, 847}}, {113, 10, 121, {1, 3, 3, 13, 9, 61, 19, 97, 47, 35}}, {114, 10, 127, {1, 1, 7, 7, 15, 29, 63, 95, 417, 469}}, {115, 10, 134, {1, 3, 1, 9, 25, 9, 71, 57, 213, 385}}, {116, 10, 140, {1, 3, 5, 13, 31, 47, 101, 57, 39, 341}}, {117, 10, 145, {1, 1, 3, 3, 31, 57, 125, 173, 365, 551}}, {118, 10, 152, {1, 3, 7, 1, 13, 57, 67, 157, 451, 707}}, {119, 10, 158, {1, 1, 1, 7, 21, 13, 105, 89, 429, 965}}, {120, 10, 161, {1, 1, 5, 9, 17, 51, 45, 119, 157, 141}}, {121, 10, 171, {1, 3, 7, 7, 13, 45, 91, 9, 129, 741}}, {122, 10, 181, {1, 3, 7, 1, 23, 57, 67, 141, 151, 571}}, {123, 10, 194, {1, 1, 3, 11, 17, 47, 93, 107, 375, 157}}, {124, 10, 199, {1, 3, 3, 5, 11, 21, 43, 51, 169, 915}}, {125, 10, 203, {1, 1, 5, 3, 15, 55, 101, 67, 455, 625}}, {126, 10, 208, {1, 3, 5, 9, 1, 23, 29, 47, 345, 595}}, {127, 10, 227, {1, 3, 7, 7, 5, 49, 29, 155, 323, 589}}, {128, 10, 242, {1, 3, 3, 7, 5, 41, 127, 61, 261, 717}}, {129, 10, 251, {1, 3, 7, 7, 17, 23, 117, 67, 129, 1009}}, {130, 10, 253, {1, 1, 3, 13, 11, 39, 21, 207, 123, 305}}, {131, 10, 265, {1, 1, 3, 9, 29, 3, 95, 47, 231, 73}}, {132, 10, 266, {1, 3, 1, 9, 1, 29, 117, 21, 441, 259}}, {133, 10, 274, {1, 3, 1, 13, 21, 39, 125, 211, 439, 723}}, {134, 10, 283, {1, 1, 7, 3, 17, 63, 115, 89, 49, 773}}, {135, 10, 289, {1, 3, 7, 13, 11, 33, 101, 107, 63, 73}}, {136, 10, 295, {1, 1, 5, 5, 13, 57, 63, 135, 437, 177}}, {137, 10, 301, {1, 1, 3, 7, 27, 63, 93, 47, 417, 483}}, {138, 10, 316, {1, 1, 3, 1, 23, 29, 1, 191, 49, 23}}, {139, 10, 319, {1, 1, 3, 15, 25, 55, 9, 101, 219, 607}}, {140, 10, 324, {1, 3, 1, 7, 7, 19, 51, 251, 393, 307}}, {141, 10, 346, {1, 3, 3, 3, 25, 55, 17, 75, 337, 3}}, {142, 10, 352, {1, 1, 1, 13, 25, 17, 65, 45, 479, 413}}, {143, 10, 361, {1, 1, 7, 7, 27, 49, 99, 161, 213, 727}}, {144, 10, 367, {1, 3, 5, 1, 23, 5, 43, 41, 251, 857}}, {145, 10, 382, {1, 3, 3, 7, 11, 61, 39, 87, 383, 835}}, {146, 10, 395, {1, 1, 3, 15, 13, 7, 29, 7, 505, 923}}, {147, 10, 398, {1, 3, 7, 1, 5, 31, 47, 157, 445, 501}}, {148, 10, 400, {1, 1, 3, 7, 1, 43, 9, 147, 115, 605}}, {149, 10, 412, {1, 3, 3, 13, 5, 1, 119, 211, 455, 1001}}, {150, 10, 419, {1, 1, 3, 5, 13, 19, 3, 243, 75, 843}}, {151, 10, 422, {1, 3, 7, 7, 1, 19, 91, 249, 357, 589}}, {152, 10, 426, {1, 1, 1, 9, 1, 25, 109, 197, 279, 411}}, {153, 10, 428, {1, 3, 1, 15, 23, 57, 59, 135, 191, 75}}, {154, 10, 433, {1, 1, 5, 15, 29, 21, 39, 253, 383, 349}}, {155, 10, 446, {1, 3, 3, 5, 19, 45, 61, 151, 199, 981}}, {156, 10, 454, {1, 3, 5, 13, 9, 61, 107, 141, 141, 1}}, {157, 10, 457, {1, 3, 1, 11, 27, 25, 85, 105, 309, 979}}, {158, 10, 472, {1, 3, 3, 11, 19, 7, 115, 223, 349, 43}}, {159, 10, 493, {1, 1, 7, 9, 21, 39, 123, 21, 275, 927}}, {160, 10, 505, {1, 1, 7, 13, 15, 41, 47, 243, 303, 437}}, {161, 10, 508, {1, 1, 1, 7, 7, 3, 15, 99, 409, 719}}, {162, 11, 2, {1, 3, 3, 15, 27, 49, 113, 123, 113, 67, 469}}, {163, 11, 11, {1, 3, 7, 11, 3, 23, 87, 169, 119, 483, 199}}, {164, 11, 21, {1, 1, 5, 15, 7, 17, 109, 229, 179, 213, 741}}, {165, 11, 22, {1, 1, 5, 13, 11, 17, 25, 135, 403, 557, 1433}}, {166, 11, 35, {1, 3, 1, 1, 1, 61, 67, 215, 189, 945, 1243}}, {167, 11, 49, {1, 1, 7, 13, 17, 33, 9, 221, 429, 217, 1679}}, {168, 11, 50, {1, 1, 3, 11, 27, 3, 15, 93, 93, 865, 1049}}, {169, 11, 56, {1, 3, 7, 7, 25, 41, 121, 35, 373, 379, 1547}}, {170, 11, 61, {1, 3, 3, 9, 11, 35, 45, 205, 241, 9, 59}}, {171, 11, 70, {1, 3, 1, 7, 3, 51, 7, 177, 53, 975, 89}}, {172, 11, 74, {1, 1, 3, 5, 27, 1, 113, 231, 299, 759, 861}}, {173, 11, 79, {1, 3, 3, 15, 25, 29, 5, 255, 139, 891, 2031}}, {174, 11, 84, {1, 3, 1, 1, 13, 9, 109, 193, 419, 95, 17}}, {175, 11, 88, {1, 1, 7, 9, 3, 7, 29, 41, 135, 839, 867}}, {176, 11, 103, {1, 1, 7, 9, 25, 49, 123, 217, 113, 909, 215}}, {177, 11, 104, {1, 1, 7, 3, 23, 15, 43, 133, 217, 327, 901}}, {178, 11, 112, {1, 1, 3, 3, 13, 53, 63, 123, 477, 711, 1387}}, {179, 11, 115, {1, 1, 3, 15, 7, 29, 75, 119, 181, 957, 247}}, {180, 11, 117, {1, 1, 1, 11, 27, 25, 109, 151, 267, 99, 1461}}, {181, 11, 122, {1, 3, 7, 15, 5, 5, 53, 145, 11, 725, 1501}}, {182, 11, 134, {1, 3, 7, 1, 9, 43, 71, 229, 157, 607, 1835}}, {183, 11, 137, {1, 3, 3, 13, 25, 1, 5, 27, 471, 349, 127}}, {184, 11, 146, {1, 1, 1, 1, 23, 37, 9, 221, 269, 897, 1685}}, {185, 11, 148, {1, 1, 3, 3, 31, 29, 51, 19, 311, 553, 1969}}, {186, 11, 157, {1, 3, 7, 5, 5, 55, 17, 39, 475, 671, 1529}}, {187, 11, 158, {1, 1, 7, 1, 1, 35, 47, 27, 437, 395, 1635}}, {188, 11, 162, {1, 1, 7, 3, 13, 23, 43, 135, 327, 139, 389}}, {189, 11, 164, {1, 3, 7, 3, 9, 25, 91, 25, 429, 219, 513}}, {190, 11, 168, {1, 1, 3, 5, 13, 29, 119, 201, 277, 157, 2043}}, {191, 11, 173, {1, 3, 5, 3, 29, 57, 13, 17, 167, 739, 1031}}, {192, 11, 185, {1, 3, 3, 5, 29, 21, 95, 27, 255, 679, 1531}}, {193, 11, 186, {1, 3, 7, 15, 9, 5, 21, 71, 61, 961, 1201}}, {194, 11, 191, {1, 3, 5, 13, 15, 57, 33, 93, 459, 867, 223}}, {195, 11, 193, {1, 1, 1, 15, 17, 43, 127, 191, 67, 177, 1073}}, {196, 11, 199, {1, 1, 1, 15, 23, 7, 21, 199, 75, 293, 1611}}, {197, 11, 213, {1, 3, 7, 13, 15, 39, 21, 149, 65, 741, 319}}, {198, 11, 214, {1, 3, 7, 11, 23, 13, 101, 89, 277, 519, 711}}, {199, 11, 220, {1, 3, 7, 15, 19, 27, 85, 203, 441, 97, 1895}}, {200, 11, 227, {1, 3, 1, 3, 29, 25, 21, 155, 11, 191, 197}}, {201, 11, 236, {1, 1, 7, 5, 27, 11, 81, 101, 457, 675, 1687}}, {202, 11, 242, {1, 3, 1, 5, 25, 5, 65, 193, 41, 567, 781}}, {203, 11, 251, {1, 3, 1, 5, 11, 15, 113, 77, 411, 695, 1111}}, {204, 11, 256, {1, 1, 3, 9, 11, 53, 119, 171, 55, 297, 509}}, {205, 11, 259, {1, 1, 1, 1, 11, 39, 113, 139, 165, 347, 595}}, {206, 11, 265, {1, 3, 7, 11, 9, 17, 101, 13, 81, 325, 1733}}, {207, 11, 266, {1, 3, 1, 1, 21, 43, 115, 9, 113, 907, 645}}, {208, 11, 276, {1, 1, 7, 3, 9, 25, 117, 197, 159, 471, 475}}, {209, 11, 292, {1, 3, 1, 9, 11, 21, 57, 207, 485, 613, 1661}}, {210, 11, 304, {1, 1, 7, 7, 27, 55, 49, 223, 89, 85, 1523}}, {211, 11, 310, {1, 1, 5, 3, 19, 41, 45, 51, 447, 299, 1355}}, {212, 11, 316, {1, 3, 1, 13, 1, 33, 117, 143, 313, 187, 1073}}, {213, 11, 319, {1, 1, 7, 7, 5, 11, 65, 97, 377, 377, 1501}}, {214, 11, 322, {1, 3, 1, 1, 21, 35, 95, 65, 99, 23, 1239}}, {215, 11, 328, {1, 1, 5, 9, 3, 37, 95, 167, 115, 425, 867}}, {216, 11, 334, {1, 3, 3, 13, 1, 37, 27, 189, 81, 679, 773}}, {217, 11, 339, {1, 1, 3, 11, 1, 61, 99, 233, 429, 969, 49}}, {218, 11, 341, {1, 1, 1, 7, 25, 63, 99, 165, 245, 793, 1143}}, {219, 11, 345, {1, 1, 5, 11, 11, 43, 55, 65, 71, 283, 273}}, {220, 11, 346, {1, 1, 5, 5, 9, 3, 101, 251, 355, 379, 1611}}, {221, 11, 362, {1, 1, 1, 15, 21, 63, 85, 99, 49, 749, 1335}}, {222, 11, 367, {1, 1, 5, 13, 27, 9, 121, 43, 255, 715, 289}}, {223, 11, 372, {1, 3, 1, 5, 27, 19, 17, 223, 77, 571, 1415}}, {224, 11, 375, {1, 1, 5, 3, 13, 59, 125, 251, 195, 551, 1737}}, {225, 11, 376, {1, 3, 3, 15, 13, 27, 49, 105, 389, 971, 755}}, {226, 11, 381, {1, 3, 5, 15, 23, 43, 35, 107, 447, 763, 253}}, {227, 11, 385, {1, 3, 5, 11, 21, 3, 17, 39, 497, 407, 611}}, {228, 11, 388, {1, 1, 7, 13, 15, 31, 113, 17, 23, 507, 1995}}, {229, 11, 392, {1, 1, 7, 15, 3, 15, 31, 153, 423, 79, 503}}, {230, 11, 409, {1, 1, 7, 9, 19, 25, 23, 171, 505, 923, 1989}}, {231, 11, 415, {1, 1, 5, 9, 21, 27, 121, 223, 133, 87, 697}}, {232, 11, 416, {1, 1, 5, 5, 9, 19, 107, 99, 319, 765, 1461}}, {233, 11, 421, {1, 1, 3, 3, 19, 25, 3, 101, 171, 729, 187}}, {234, 11, 428, {1, 1, 3, 1, 13, 23, 85, 93, 291, 209, 37}}, {235, 11, 431, {1, 1, 1, 15, 25, 25, 77, 253, 333, 947, 1073}}, {236, 11, 434, {1, 1, 3, 9, 17, 29, 55, 47, 255, 305, 2037}}, {237, 11, 439, {1, 3, 3, 9, 29, 63, 9, 103, 489, 939, 1523}}, {238, 11, 446, {1, 3, 7, 15, 7, 31, 89, 175, 369, 339, 595}}, {239, 11, 451, {1, 3, 7, 13, 25, 5, 71, 207, 251, 367, 665}}, {240, 11, 453, {1, 3, 3, 3, 21, 25, 75, 35, 31, 321, 1603}}, {241, 11, 457, {1, 1, 1, 9, 11, 1, 65, 5, 11, 329, 535}}, {242, 11, 458, {1, 1, 5, 3, 19, 13, 17, 43, 379, 485, 383}}, {243, 11, 471, {1, 3, 5, 13, 13, 9, 85, 147, 489, 787, 1133}}, {244, 11, 475, {1, 3, 1, 1, 5, 51, 37, 129, 195, 297, 1783}}, {245, 11, 478, {1, 1, 3, 15, 19, 57, 59, 181, 455, 697, 2033}}, {246, 11, 484, {1, 3, 7, 1, 27, 9, 65, 145, 325, 189, 201}}, {247, 11, 493, {1, 3, 1, 15, 31, 23, 19, 5, 485, 581, 539}}, {248, 11, 494, {1, 1, 7, 13, 11, 15, 65, 83, 185, 847, 831}}, {249, 11, 499, {1, 3, 5, 7, 7, 55, 73, 15, 303, 511, 1905}}, {250, 11, 502, {1, 3, 5, 9, 7, 21, 45, 15, 397, 385, 597}}, {251, 11, 517, {1, 3, 7, 3, 23, 13, 73, 221, 511, 883, 1265}}, {252, 11, 518, {1, 1, 3, 11, 1, 51, 73, 185, 33, 975, 1441}}, {253, 11, 524, {1, 3, 3, 9, 19, 59, 21, 39, 339, 37, 143}}, {254, 11, 527, {1, 1, 7, 1, 31, 33, 19, 167, 117, 635, 639}}, {255, 11, 555, {1, 1, 1, 3, 5, 13, 59, 83, 355, 349, 1967}}, {256, 11, 560, {1, 1, 1, 5, 19, 3, 53, 133, 97, 863, 983}}, {257, 11, 565, {1, 3, 1, 13, 9, 41, 91, 105, 173, 97, 625}}, {258, 11, 569, {1, 1, 5, 3, 7, 49, 115, 133, 71, 231, 1063}}, {259, 11, 578, {1, 1, 7, 5, 17, 43, 47, 45, 497, 547, 757}}, {260, 11, 580, {1, 3, 5, 15, 21, 61, 123, 191, 249, 31, 631}}, {261, 11, 587, {1, 3, 7, 9, 17, 7, 11, 185, 127, 169, 1951}}, {262, 11, 589, {1, 1, 5, 13, 11, 11, 9, 49, 29, 125, 791}}, {263, 11, 590, {1, 1, 1, 15, 31, 41, 13, 167, 273, 429, 57}}, {264, 11, 601, {1, 3, 5, 3, 27, 7, 35, 209, 65, 265, 1393}}, {265, 11, 607, {1, 3, 1, 13, 31, 19, 53, 143, 135, 9, 1021}}, {266, 11, 611, {1, 1, 7, 13, 31, 5, 115, 153, 143, 957, 623}}, {267, 11, 614, {1, 1, 5, 11, 25, 19, 29, 31, 297, 943, 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9, 9, 5, 45, 135, 115, 181, 1685, 3505, 4387}}, {1060, 13, 3750, {1, 1, 1, 1, 19, 35, 69, 113, 305, 419, 949, 2969, 247}}, {1061, 13, 3762, {1, 1, 5, 13, 23, 61, 13, 139, 501, 811, 67, 1501, 6493}}, {1062, 13, 3764, {1, 1, 3, 13, 15, 41, 27, 217, 293, 13, 145, 2631, 6991}}, {1063, 13, 3774, {1, 3, 3, 13, 15, 37, 71, 123, 285, 49, 627, 1283, 5993}}, {1064, 13, 3776, {1, 3, 3, 11, 9, 25, 11, 1, 203, 353, 1347, 1999, 2799}}, {1065, 13, 3786, {1, 3, 5, 1, 7, 49, 101, 231, 499, 63, 1977, 2207, 7829}}, {1066, 13, 3800, {1, 1, 7, 1, 17, 15, 115, 139, 381, 943, 623, 4037, 2971}}, {1067, 13, 3803, {1, 1, 3, 5, 13, 55, 23, 87, 139, 795, 1669, 1375, 1185}}, {1068, 13, 3809, {1, 3, 3, 5, 5, 45, 97, 253, 241, 333, 645, 555, 7867}}, {1069, 13, 3816, {1, 3, 5, 1, 1, 1, 89, 27, 407, 509, 1433, 609, 2355}}, {1070, 13, 3821, {1, 3, 7, 1, 27, 29, 5, 157, 495, 811, 1293, 1143, 827}}, {1071, 13, 3827, {1, 1, 3, 3, 25, 49, 127, 111, 191, 3, 845, 1383, 2521}}, {1072, 13, 3829, {1, 1, 5, 7, 5, 51, 101, 155, 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81, 53, 215, 587, 167, 4045, 5671, 5597, 13529}}, {1884, 15, 128, {1, 3, 5, 15, 1, 9, 59, 235, 315, 195, 909, 2237, 505, 10415, 28145}}, {1885, 15, 138, {1, 1, 1, 3, 9, 31, 41, 43, 275, 921, 25, 671, 5737, 11241, 4193}}, {1886, 15, 146, {1, 3, 3, 13, 29, 13, 95, 213, 317, 995, 1489, 3779, 3043, 8569, 28823}}, {1887, 15, 171, {1, 1, 7, 5, 9, 49, 125, 241, 87, 153, 1673, 3849, 7253, 1715, 11627}}, {1888, 15, 174, {1, 1, 3, 9, 27, 27, 19, 223, 63, 463, 1095, 1395, 6643, 11589, 2145}}, {1889, 15, 176, {1, 1, 3, 15, 21, 17, 45, 23, 357, 11, 1307, 1791, 2481, 2123, 24341}}, {1890, 15, 182, {1, 3, 5, 15, 31, 53, 117, 51, 433, 193, 1239, 3329, 2403, 12745, 32219}}, {1891, 15, 194, {1, 1, 5, 9, 7, 27, 9, 115, 417, 579, 83, 173, 4717, 15665, 27463}}, {1892, 15, 208, {1, 3, 5, 7, 9, 9, 31, 35, 249, 567, 331, 905, 5101, 14817, 14255}}, {1893, 15, 211, {1, 3, 7, 3, 1, 61, 29, 129, 119, 421, 1597, 2987, 3041, 7629, 23451}}, {1894, 15, 220, {1, 1, 7, 9, 13, 1, 99, 105, 107, 509, 989, 2259, 1009, 6827, 8903}}, {1895, 15, 229, {1, 3, 5, 15, 11, 29, 85, 29, 265, 105, 2035, 3349, 3543, 13903, 10213}}, {1896, 15, 230, {1, 3, 1, 1, 25, 19, 53, 139, 467, 485, 491, 3067, 7353, 13861, 25819}}, {1897, 15, 239, {1, 1, 5, 3, 3, 43, 41, 185, 45, 463, 351, 2823, 2519, 6705, 11395}}, {1898, 15, 254, {1, 3, 7, 13, 11, 15, 87, 221, 427, 673, 1631, 599, 3259, 10691, 31283}}, {1899, 15, 265, {1, 3, 5, 11, 9, 9, 15, 49, 275, 335, 1613, 3587, 5309, 14849, 26475}}, {1900, 15, 285, {1, 3, 7, 9, 29, 13, 79, 225, 381, 781, 1411, 2761, 7157, 14983, 19717}}, {1901, 15, 290, {1, 1, 7, 11, 29, 25, 117, 183, 101, 651, 653, 3157, 445, 14389, 23293}}, {1902, 15, 319, {1, 1, 1, 3, 5, 33, 73, 155, 473, 387, 591, 2045, 5965, 16299, 31499}}, {1903, 15, 324, {1, 3, 1, 7, 11, 33, 29, 21, 491, 937, 729, 4075, 975, 2461, 18991}}, {1904, 15, 327, {1, 3, 7, 15, 29, 39, 105, 111, 173, 943, 69, 295, 8175, 13037, 26131}}, {1905, 15, 333, {1, 1, 5, 15, 7, 5, 97, 147, 105, 887, 443, 2595, 5889, 10753, 1619}}, {1906, 15, 357, {1, 3, 3, 15, 11, 45, 87, 207, 353, 909, 1847, 323, 2283, 12885, 16415}}, {1907, 15, 364, {1, 1, 5, 3, 19, 33, 43, 79, 115, 653, 359, 2873, 4609, 12439, 6339}}, {1908, 15, 395, {1, 3, 7, 9, 17, 61, 49, 227, 291, 69, 1753, 3899, 483, 3187, 29041}}, {1909, 15, 397, {1, 3, 5, 3, 25, 35, 61, 211, 393, 199, 691, 1779, 6295, 13371, 15817}}, {1910, 15, 405, {1, 3, 7, 5, 7, 23, 37, 91, 245, 915, 579, 867, 6193, 1063, 17363}}, {1911, 15, 409, {1, 3, 7, 7, 23, 51, 41, 63, 375, 3, 159, 1889, 4419, 1687, 17977}}, {1912, 15, 419, {1, 1, 1, 7, 13, 11, 53, 43, 317, 325, 1749, 2423, 4123, 8595, 20773}}, {1913, 15, 422, {1, 1, 7, 7, 9, 9, 61, 113, 437, 213, 1407, 645, 4345, 807, 30411}}, {1914, 15, 431, {1, 3, 3, 11, 17, 39, 17, 113, 391, 385, 581, 2023, 7449, 10153, 22033}}, {1915, 15, 433, {1, 1, 3, 5, 29, 31, 101, 215, 379, 377, 1113, 2855, 7147, 14377, 25515}}, {1916, 15, 436, {1, 3, 5, 5, 13, 3, 121, 125, 227, 969, 11, 1115, 5657, 9209, 6117}}, {1917, 15, 440, {1, 3, 7, 15, 29, 17, 33, 123, 317, 301, 749, 1365, 5619, 605, 1613}}, {1918, 15, 453, {1, 3, 1, 15, 7, 53, 125, 249, 219, 655, 105, 2825, 1649, 12783, 19777}}, {1919, 15, 460, {1, 1, 7, 1, 25, 53, 19, 53, 157, 373, 1855, 495, 5065, 9465, 2313}}, {1920, 15, 471, {1, 3, 5, 13, 3, 57, 57, 161, 431, 415, 1859, 1033, 6349, 1577, 31579}}, {1921, 15, 478, {1, 1, 7, 5, 23, 63, 29, 221, 13, 965, 1997, 2265, 1583, 10491, 9551}}, {1922, 15, 482, {1, 1, 3, 13, 31, 25, 23, 61, 285, 5, 2005, 879, 795, 13299, 19685}}, {1923, 15, 488, {1, 1, 7, 1, 21, 45, 121, 89, 263, 543, 1333, 2711, 219, 10823, 26139}}, {1924, 15, 524, {1, 1, 3, 3, 27, 13, 19, 117, 161, 457, 1541, 295, 4953, 12125, 14503}}, {1925, 15, 529, {1, 3, 5, 3, 7, 63, 13, 247, 439, 681, 977, 2537, 6923, 10323, 7349}}, {1926, 15, 535, {1, 3, 5, 9, 3, 51, 81, 251, 349, 983, 581, 2515, 2281, 2849, 31915}}, {1927, 15, 536, {1, 3, 5, 3, 11, 63, 47, 137, 303, 627, 91, 2269, 7097, 2145, 31059}}, {1928, 15, 539, {1, 1, 3, 15, 13, 17, 53, 27, 133, 13, 117, 1837, 4103, 5843, 29153}}, {1929, 15, 563, {1, 1, 5, 13, 21, 33, 37, 253, 465, 209, 309, 49, 3209, 15677, 14569}}, {1930, 15, 566, {1, 1, 7, 15, 13, 21, 33, 203, 499, 141, 1155, 3893, 1663, 2115, 27459}}, {1931, 15, 572, {1, 3, 5, 11, 21, 9, 39, 157, 257, 273, 1257, 1831, 515, 7969, 20133}}, {1932, 15, 577, {1, 1, 3, 13, 19, 29, 15, 189, 103, 219, 1395, 517, 7425, 6585, 15865}}, {1933, 15, 587, {1, 1, 5, 11, 21, 31, 49, 151, 39, 537, 1783, 3449, 6915, 223, 11587}}, {1934, 15, 592, {1, 3, 3, 11, 7, 63, 69, 31, 27, 911, 1903, 2821, 7977, 12949, 32257}}, {1935, 15, 602, {1, 1, 7, 9, 25, 45, 23, 233, 511, 595, 1383, 1721, 6789, 12055, 21179}}, {1936, 15, 623, {1, 1, 7, 13, 1, 27, 123, 49, 439, 683, 501, 641, 1947, 6111, 25423}}, {1937, 15, 635, {1, 3, 3, 5, 1, 23, 57, 241, 243, 593, 2039, 1617, 2209, 5171, 9675}}, {1938, 15, 638, {1, 1, 1, 7, 5, 19, 83, 55, 481, 125, 177, 1021, 1139, 11403, 23099}}, {1939, 15, 654, {1, 1, 3, 5, 29, 39, 33, 217, 461, 907, 733, 3795, 4811, 12939, 27715}}, {1940, 15, 656, {1, 3, 7, 3, 7, 11, 39, 165, 495, 147, 999, 1827, 817, 603, 9293}}, {1941, 15, 659, {1, 3, 7, 15, 25, 53, 35, 15, 431, 733, 1213, 2907, 8087, 3939, 27363}}, {1942, 15, 665, {1, 3, 7, 13, 13, 9, 33, 27, 485, 183, 455, 3341, 2555, 4985, 8793}}, {1943, 15, 675, {1, 1, 1, 15, 25, 47, 75, 21, 205, 15, 1639, 3067, 1295, 11693, 16903}}, {1944, 15, 677, {1, 1, 1, 15, 3, 31, 93, 57, 43, 185, 251, 1899, 7885, 10829, 3609}}, {1945, 15, 687, {1, 1, 3, 1, 29, 9, 69, 223, 221, 537, 365, 3411, 5771, 15279, 5309}}, {1946, 15, 696, {1, 1, 7, 5, 1, 5, 125, 243, 213, 1003, 1571, 3355, 3981, 8781, 25993}}, {1947, 15, 701, {1, 1, 1, 13, 7, 19, 53, 243, 301, 75, 1183, 2723, 6687, 13, 16581}}, {1948, 15, 704, {1, 3, 1, 13, 17, 51, 91, 239, 437, 191, 1065, 2495, 5755, 3405, 8299}}, {1949, 15, 710, {1, 1, 5, 5, 11, 59, 21, 169, 299, 123, 1845, 2199, 2157, 14461, 10327}}, {1950, 15, 721, {1, 3, 7, 7, 19, 47, 51, 179, 41, 19, 1347, 2325, 8063, 5993, 15653}}, {1951, 15, 728, {1, 1, 1, 9, 25, 27, 7, 133, 223, 533, 719, 353, 7093, 8285, 10375}}, {1952, 15, 738, {1, 3, 5, 15, 31, 5, 67, 39, 441, 495, 977, 3699, 1435, 11385, 14567}}, {1953, 15, 740, {1, 1, 3, 15, 15, 39, 25, 33, 91, 523, 249, 4035, 769, 5181, 9691}}, {1954, 15, 749, {1, 1, 3, 3, 3, 57, 83, 187, 423, 165, 161, 3453, 2241, 981, 8429}}, {1955, 15, 758, {1, 1, 7, 15, 1, 17, 57, 189, 283, 11, 823, 3505, 7025, 11879, 15441}}, {1956, 15, 761, {1, 1, 3, 11, 1, 41, 7, 255, 385, 339, 607, 1405, 1473, 13697, 9491}}, {1957, 15, 772, {1, 1, 7, 15, 5, 9, 91, 99, 211, 233, 51, 2663, 1165, 9283, 18495}}, {1958, 15, 776, {1, 1, 3, 7, 21, 37, 13, 91, 39, 27, 1021, 2813, 5937, 6645, 3403}}, {1959, 15, 782, {1, 3, 1, 1, 29, 29, 5, 69, 399, 665, 1407, 3921, 2653, 11753, 18925}}, {1960, 15, 789, {1, 3, 7, 15, 13, 41, 39, 1, 437, 549, 161, 2315, 5631, 8335, 22661}}, {1961, 15, 810, {1, 1, 3, 1, 7, 17, 115, 61, 69, 955, 475, 3763, 8035, 927, 17893}}, {1962, 15, 812, {1, 3, 1, 13, 21, 59, 81, 145, 463, 145, 1941, 2777, 7453, 14229, 11281}}, {1963, 15, 818, {1, 1, 1, 15, 15, 11, 27, 165, 461, 395, 1645, 3611, 7463, 12379, 26787}}, {1964, 15, 830, {1, 1, 7, 9, 29, 19, 27, 123, 21, 149, 1643, 4001, 7207, 6769, 4647}}, {1965, 15, 832, {1, 1, 1, 11, 13, 9, 103, 139, 185, 587, 591, 1113, 2223, 11667, 32671}}, {1966, 15, 852, {1, 3, 1, 1, 31, 13, 19, 93, 229, 125, 1471, 2369, 3055, 10277, 28563}}, {1967, 15, 855, {1, 3, 7, 5, 7, 53, 99, 175, 161, 851, 617, 4027, 2357, 11199, 1931}}, {1968, 15, 859, {1, 3, 5, 11, 3, 31, 111, 179, 237, 845, 539, 1057, 259, 3417, 26637}}, {1969, 15, 865, {1, 1, 5, 3, 21, 49, 125, 119, 463, 403, 737, 1811, 3941, 13015, 29081}}, {1970, 15, 877, {1, 3, 5, 13, 5, 29, 69, 251, 313, 357, 663, 1097, 3307, 12845, 28495}}, {1971, 15, 895, {1, 3, 3, 5, 29, 17, 89, 15, 411, 409, 2013, 757, 4085, 12521, 11131}}, {1972, 15, 901, {1, 1, 1, 15, 7, 51, 3, 193, 493, 133, 381, 2027, 227, 6635, 12931}}, {1973, 15, 902, {1, 1, 1, 15, 7, 23, 99, 203, 323, 1007, 1465, 2887, 2215, 1787, 22069}}, {1974, 15, 906, {1, 1, 5, 9, 29, 59, 77, 151, 509, 313, 415, 3977, 5431, 8019, 8571}}, {1975, 15, 916, {1, 3, 1, 15, 19, 13, 57, 217, 87, 119, 25, 1149, 5667, 3765, 6959}}, {1976, 15, 920, {1, 3, 7, 13, 19, 31, 119, 3, 457, 117, 905, 361, 1483, 12405, 27005}}, {1977, 15, 949, {1, 3, 5, 11, 15, 35, 61, 77, 119, 51, 1753, 2765, 1091, 10573, 23595}}, {1978, 15, 962, {1, 3, 3, 7, 1, 35, 17, 93, 197, 511, 1253, 3031, 2739, 15127, 15147}}, {1979, 15, 964, {1, 3, 3, 1, 11, 55, 55, 107, 161, 75, 129, 2195, 2023, 4877, 25797}}, {1980, 15, 967, {1, 3, 5, 7, 23, 19, 113, 167, 167, 271, 1303, 125, 5057, 1323, 5165}}, {1981, 15, 981, {1, 1, 5, 3, 21, 31, 11, 119, 215, 483, 1535, 407, 6485, 15401, 30297}}, {1982, 15, 982, {1, 3, 5, 9, 21, 5, 77, 95, 443, 247, 913, 605, 365, 7465, 19707}}, {1983, 15, 985, {1, 3, 1, 7, 17, 59, 9, 35, 391, 767, 1493, 475, 4725, 7529, 31579}}, {1984, 15, 991, {1, 3, 3, 7, 31, 21, 61, 31, 421, 179, 273, 771, 5745, 10575, 32765}}, {1985, 15, 1007, {1, 3, 5, 15, 27, 13, 125, 55, 423, 1021, 497, 3521, 6903, 15111, 8285}}, {1986, 15, 1016, {1, 1, 5, 9, 13, 31, 105, 93, 421, 709, 643, 1079, 1533, 9149, 10799}}, {1987, 15, 1024, {1, 3, 1, 11, 19, 29, 53, 199, 319, 247, 655, 3039, 6411, 12267, 14245}}, {1988, 15, 1051, {1, 3, 1, 11, 9, 57, 5, 91, 469, 149, 259, 329, 5433, 6941, 15093}}, {1989, 15, 1060, {1, 3, 1, 5, 5, 51, 59, 25, 455, 367, 1623, 441, 3155, 11695, 20767}}, {1990, 15, 1070, {1, 3, 7, 7, 11, 49, 113, 95, 91, 389, 605, 1973, 2051, 2315, 22229}}, {1991, 15, 1072, {1, 3, 5, 3, 19, 11, 99, 135, 433, 781, 1473, 885, 1105, 3573, 3739}}, {1992, 15, 1084, {1, 3, 1, 11, 3, 25, 9, 227, 433, 723, 317, 139, 6627, 8067, 28439}}, {1993, 15, 1089, {1, 1, 1, 9, 9, 9, 5, 63, 241, 215, 1991, 2949, 3943, 775, 31511}}, {1994, 15, 1095, {1, 1, 3, 7, 17, 49, 35, 167, 131, 107, 1295, 2465, 4577, 11147, 29833}}, {1995, 15, 1114, {1, 1, 5, 1, 5, 25, 119, 129, 391, 743, 1069, 2957, 349, 6891, 13635}}, {1996, 15, 1123, {1, 3, 1, 7, 9, 31, 63, 253, 215, 51, 1347, 2361, 3125, 13049, 28461}}, {1997, 15, 1132, {1, 1, 7, 9, 3, 31, 21, 163, 255, 47, 259, 535, 5461, 3349, 30649}}, {1998, 15, 1154, {1, 3, 3, 13, 17, 33, 87, 47, 243, 709, 929, 3943, 3107, 3421, 13721}}, {1999, 15, 1156, {1, 3, 5, 11, 25, 61, 61, 173, 397, 735, 2005, 3355, 8121, 11593, 27697}}, {2000, 15, 1163, {1, 3, 5, 15, 17, 43, 63, 231, 275, 311, 1277, 2669, 7307, 2099, 9755}}, {2001, 15, 1171, {1, 3, 5, 3, 25, 43, 71, 191, 9, 121, 1873, 3747, 7491, 14055, 24293}}, {2002, 15, 1202, {1, 3, 5, 13, 17, 35, 113, 113, 385, 941, 39, 2705, 1225, 5167, 1373}}, {2003, 15, 1228, {1, 3, 5, 5, 7, 35, 19, 105, 487, 71, 139, 627, 4187, 3183, 713}}, {2004, 15, 1239, {1, 1, 5, 13, 29, 29, 103, 5, 157, 869, 1675, 423, 6689, 10697, 5303}}, {2005, 15, 1255, {1, 1, 5, 1, 29, 31, 61, 111, 473, 963, 685, 1483, 2383, 8109, 8495}}, {2006, 15, 1256, {1, 1, 5, 3, 19, 13, 95, 113, 217, 59, 1353, 1647, 3617, 3271, 2321}}, {2007, 15, 1262, {1, 3, 5, 7, 25, 35, 59, 131, 309, 445, 415, 93, 1453, 8789, 30201}}, {2008, 15, 1270, {1, 1, 5, 1, 5, 43, 71, 241, 123, 189, 831, 3469, 8093, 6187, 32721}}, {2009, 15, 1279, {1, 3, 7, 5, 25, 31, 123, 171, 319, 379, 889, 2365, 4881, 12225, 16609}}, {2010, 15, 1308, {1, 3, 1, 11, 27, 43, 121, 63, 291, 591, 811, 1995, 4777, 2083, 31385}}, {2011, 15, 1322, {1, 1, 5, 11, 27, 53, 85, 187, 461, 823, 703, 399, 6925, 11517, 28697}}, {2012, 15, 1329, {1, 1, 3, 5, 13, 11, 33, 121, 93, 717, 1275, 3877, 4247, 5845, 26909}}, {2013, 15, 1330, {1, 3, 1, 9, 7, 5, 47, 199, 367, 561, 185, 2855, 5997, 2699, 7581}}, {2014, 15, 1336, {1, 1, 5, 9, 23, 11, 71, 201, 61, 729, 1011, 3529, 663, 1413, 25675}}, {2015, 15, 1341, {1, 3, 7, 13, 27, 21, 11, 127, 281, 487, 1217, 3129, 5541, 3129, 17783}}, {2016, 15, 1347, {1, 1, 5, 9, 1, 29, 85, 193, 213, 743, 1473, 611, 391, 9405, 21137}}, {2017, 15, 1349, {1, 3, 3, 3, 31, 63, 37, 147, 39, 351, 79, 3069, 2441, 8901, 8777}}, {2018, 15, 1359, {1, 1, 7, 7, 25, 49, 55, 47, 441, 343, 1267, 1123, 5917, 14395, 10579}}, {2019, 15, 1367, {1, 1, 7, 1, 13, 55, 55, 123, 103, 773, 125, 2145, 4743, 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66221, 221691}}, {21083, 18, 129026, {1, 3, 7, 13, 21, 15, 59, 67, 441, 113, 1229, 1587, 5889, 6691, 10641, 11865, 89791, 82867}}, {21084, 18, 129055, {1, 1, 7, 9, 13, 21, 53, 145, 235, 877, 2005, 1005, 7137, 6091, 19611, 25959, 124019, 216269}}, {21085, 18, 129071, {1, 3, 7, 9, 17, 63, 5, 245, 397, 351, 1613, 4079, 7235, 4397, 18951, 11609, 71593, 148615}}, {21086, 18, 129093, {1, 3, 3, 11, 5, 59, 65, 221, 237, 527, 861, 397, 249, 15273, 8415, 61185, 59419, 98115}}, {21087, 18, 129105, {1, 1, 3, 5, 5, 59, 17, 247, 3, 765, 835, 1131, 3985, 9021, 18067, 28525, 86513, 250227}}, {21088, 18, 129124, {1, 3, 7, 15, 25, 47, 119, 143, 143, 283, 1791, 59, 8171, 12577, 17079, 9809, 100299, 63977}}, {21089, 18, 129148, {1, 3, 5, 13, 1, 47, 93, 159, 199, 863, 1279, 77, 4719, 3623, 30713, 39271, 126299, 130297}}, {21090, 18, 129151, {1, 1, 5, 3, 23, 11, 119, 187, 57, 373, 747, 1507, 5165, 12929, 903, 49041, 70215, 117113}}, {21091, 18, 129155, {1, 1, 5, 1, 3, 59, 23, 77, 151, 77, 627, 2865, 7055, 10469, 12095, 20481, 13429, 47573}}, {21092, 18, 129161, {1, 3, 1, 13, 27, 13, 115, 233, 343, 407, 1321, 4011, 5589, 15369, 23495, 4435, 75421, 229325}}, {21093, 18, 129200, {1, 3, 3, 3, 5, 51, 89, 53, 275, 279, 203, 2829, 4415, 4735, 25417, 17633, 99445, 183945}}, {21094, 18, 129224, {1, 3, 3, 15, 7, 9, 91, 63, 143, 945, 453, 4001, 3943, 7285, 9359, 27507, 8571, 31827}}, {21095, 18, 129230, {1, 3, 3, 11, 15, 49, 103, 25, 273, 791, 145, 2203, 4721, 7709, 25085, 33937, 98693, 97445}}, {21096, 18, 129237, {1, 1, 5, 15, 9, 13, 87, 27, 331, 137, 1031, 585, 7841, 12213, 32259, 46953, 17813, 203379}}, {21097, 18, 129298, {1, 3, 1, 5, 29, 53, 121, 179, 21, 311, 991, 2145, 6577, 12889, 8763, 46629, 128093, 105033}}, {21098, 18, 129300, {1, 3, 1, 9, 7, 29, 57, 137, 333, 109, 615, 749, 2665, 13087, 13989, 41857, 102937, 125183}}, {21099, 18, 129316, {1, 1, 5, 5, 3, 23, 107, 5, 319, 503, 1209, 47, 349, 11681, 28521, 44707, 112887, 232275}}, {21100, 18, 129345, {1, 3, 3, 13, 13, 51, 13, 5, 293, 15, 555, 135, 2565, 13325, 30411, 14837, 65591, 249205}}, {21101, 18, 129351, {1, 3, 5, 13, 17, 3, 73, 255, 447, 699, 503, 3655, 7735, 12163, 6167, 15027, 103831, 146395}}, {21102, 18, 129352, {1, 3, 1, 13, 5, 9, 27, 45, 397, 463, 1739, 3193, 6731, 7533, 11217, 22359, 82603, 231613}}, {21103, 18, 129363, {1, 1, 3, 15, 5, 43, 73, 191, 53, 187, 1905, 745, 1571, 9013, 8515, 59527, 104671, 227063}}, {21104, 18, 129393, {1, 1, 3, 1, 5, 47, 57, 179, 433, 979, 147, 1701, 4019, 6855, 24487, 65495, 69919, 6659}}, {21105, 18, 129410, {1, 3, 3, 1, 17, 17, 13, 75, 163, 781, 421, 1573, 2519, 9243, 20693, 60909, 65661, 208125}}, {21106, 18, 129415, {1, 3, 5, 7, 27, 57, 39, 79, 157, 415, 729, 3651, 3581, 9443, 6409, 45993, 99051, 140977}}, {21107, 18, 129449, {1, 3, 3, 13, 1, 7, 109, 77, 423, 185, 97, 3719, 2355, 10593, 2421, 37339, 24961, 24305}}, {21108, 18, 129477, {1, 3, 5, 13, 17, 7, 125, 43, 453, 43, 643, 3757, 3721, 16083, 20871, 26451, 95201, 29153}}, {21109, 18, 129501, {1, 1, 7, 3, 13, 49, 99, 253, 59, 21, 445, 3677, 6683, 2165, 32367, 55249, 5991, 155033}}, {21110, 18, 129518, {1, 1, 3, 9, 21, 9, 15, 219, 175, 631, 665, 2455, 4701, 10639, 13907, 26937, 58867, 259861}}, {21111, 18, 129520, {1, 3, 5, 5, 23, 5, 39, 233, 27, 811, 1435, 625, 4703, 3699, 20763, 50047, 123875, 10129}}, {21112, 18, 129545, {1, 1, 7, 5, 23, 1, 49, 223, 309, 691, 953, 575, 5279, 10515, 11519, 35387, 48417, 134001}}, {21113, 18, 129563, {1, 1, 7, 11, 3, 15, 125, 109, 39, 713, 1823, 1613, 4347, 6839, 29511, 26865, 102077, 31425}}, {21114, 18, 129594, {1, 1, 1, 7, 31, 43, 13, 221, 115, 993, 1155, 1641, 1063, 2065, 18909, 45769, 65331, 188455}}, {21115, 18, 129608, {1, 1, 7, 13, 21, 9, 59, 7, 79, 217, 2009, 667, 7685, 14761, 20149, 44133, 41037, 78369}}, {21116, 18, 129616, {1, 3, 1, 9, 23, 57, 1, 193, 77, 681, 1135, 3657, 8149, 3559, 25011, 55027, 121903, 240157}}, {21117, 18, 129652, {1, 3, 3, 5, 31, 41, 59, 5, 159, 627, 1569, 23, 2311, 2239, 20811, 54931, 130949, 193071}}, {21118, 18, 129659, {1, 1, 1, 1, 27, 45, 43, 1, 381, 801, 451, 1361, 1611, 5379, 27819, 8949, 4953, 222335}}, {21119, 18, 129680, {1, 1, 7, 7, 7, 11, 101, 17, 197, 561, 297, 159, 7443, 7273, 819, 23487, 24927, 151781}}, {21120, 18, 129692, {1, 3, 1, 3, 15, 43, 119, 193, 205, 835, 7, 689, 8045, 11167, 19521, 65075, 87265, 53669}}, {21121, 18, 129738, {1, 3, 7, 7, 9, 51, 43, 209, 239, 415, 995, 4037, 1219, 2683, 30459, 36161, 111157, 184551}}, {21122, 18, 129764, {1, 3, 7, 11, 27, 3, 81, 43, 407, 463, 231, 3545, 2691, 5235, 22053, 37233, 98757, 149111}}, {21123, 18, 129782, {1, 3, 1, 5, 17, 25, 47, 185, 487, 403, 1063, 1445, 4457, 15443, 11693, 54823, 131001, 9813}}, {21124, 18, 129793, {1, 3, 5, 3, 5, 35, 127, 253, 173, 491, 133, 3575, 1981, 12735, 26021, 61615, 74615, 159829}}, {21125, 18, 129820, {1, 1, 5, 9, 13, 37, 67, 155, 317, 389, 603, 4061, 3527, 9315, 32331, 43145, 82511, 240133}}, {21126, 18, 129824, {1, 1, 5, 1, 21, 41, 89, 3, 61, 627, 1301, 2073, 447, 8139, 2509, 52075, 50687, 240239}}, {21127, 18, 129829, {1, 3, 7, 13, 25, 61, 117, 107, 175, 7, 1173, 561, 5777, 10525, 20713, 34987, 48005, 214361}}, {21128, 18, 129848, {1, 3, 7, 15, 25, 31, 127, 147, 177, 881, 95, 2115, 4765, 10485, 9253, 721, 193, 222459}}, {21129, 18, 129854, {1, 3, 5, 3, 3, 13, 47, 77, 441, 1001, 215, 2365, 3603, 405, 11401, 14523, 65755, 258229}}, {21130, 18, 129861, {1, 1, 3, 9, 19, 29, 71, 153, 77, 613, 1815, 2033, 1821, 15497, 18805, 28851, 88247, 143115}}, {21131, 18, 129879, {1, 3, 1, 11, 21, 19, 37, 35, 427, 887, 1977, 1961, 3619, 10739, 30115, 55937, 102045, 110929}}, {21132, 18, 129886, {1, 3, 3, 13, 21, 27, 49, 15, 405, 629, 2015, 867, 2121, 13789, 19225, 22343, 105629, 123113}}, {21133, 18, 129907, {1, 1, 1, 1, 17, 19, 55, 207, 507, 1001, 1753, 315, 2799, 8643, 1519, 4057, 16599, 222223}}, {21134, 18, 129949, {1, 1, 5, 7, 21, 37, 63, 53, 103, 261, 595, 389, 6041, 11127, 23625, 61683, 80953, 255891}}, {21135, 18, 129953, {1, 1, 1, 5, 25, 21, 81, 233, 79, 57, 1311, 3965, 7747, 687, 32149, 397, 4551, 37657}}, {21136, 18, 129980, {1, 1, 1, 5, 9, 19, 87, 67, 325, 157, 317, 591, 1401, 8275, 20413, 39529, 75349, 183679}}, {21137, 18, 129998, {1, 3, 3, 15, 9, 3, 83, 205, 195, 599, 829, 3109, 3705, 13991, 8781, 41555, 31689, 86933}}, {21138, 18, 130031, {1, 3, 5, 1, 3, 9, 37, 235, 271, 883, 561, 1473, 7693, 177, 14113, 19507, 75221, 67517}}, {21139, 18, 130043, {1, 1, 1, 9, 7, 29, 87, 189, 239, 429, 537, 1657, 6373, 2449, 17621, 19649, 77235, 102775}}, {21140, 18, 130057, {1, 1, 7, 7, 1, 43, 69, 207, 241, 561, 1809, 3119, 4657, 15797, 18751, 52169, 105005, 172657}}, {21141, 18, 130065, {1, 1, 7, 5, 5, 59, 67, 231, 27, 435, 1073, 2689, 229, 733, 1579, 52289, 110285, 76721}}, {21142, 18, 130087, {1, 3, 5, 9, 31, 19, 87, 41, 489, 705, 1363, 963, 5865, 8237, 10295, 43169, 81561, 177209}}, {21143, 18, 130091, {1, 3, 3, 1, 25, 39, 63, 255, 403, 625, 1601, 71, 6609, 4165, 21987, 31269, 25473, 17063}}, {21144, 18, 130096, {1, 3, 3, 11, 19, 13, 101, 245, 17, 687, 1037, 3345, 7257, 13081, 5131, 29003, 72319, 223505}}, {21145, 18, 130101, {1, 3, 3, 3, 11, 49, 107, 29, 463, 465, 977, 4007, 2121, 4821, 1465, 53725, 36783, 247057}}, {21146, 18, 130111, {1, 1, 1, 3, 1, 43, 71, 49, 261, 965, 1041, 3951, 3791, 2503, 26009, 52039, 4639, 141281}}, {21147, 18, 130126, {1, 1, 3, 5, 29, 45, 79, 33, 119, 491, 1403, 1637, 853, 5609, 29853, 16435, 117877, 58443}}, {21148, 18, 130137, {1, 1, 3, 5, 13, 17, 109, 187, 201, 705, 235, 1485, 7673, 6335, 3341, 20451, 64697, 129519}}, {21149, 18, 130138, {1, 1, 7, 13, 11, 41, 95, 81, 135, 783, 1293, 2095, 3599, 10175, 3205, 56915, 131, 19281}}, {21150, 18, 130149, {1, 3, 5, 9, 13, 19, 53, 223, 283, 733, 1915, 3029, 2779, 8133, 28163, 37263, 91245, 1927}}, {21151, 18, 130177, {1, 3, 3, 3, 1, 55, 41, 123, 209, 195, 1423, 2467, 3809, 11169, 23593, 8703, 40975, 175651}}, {21152, 18, 130180, {1, 3, 7, 9, 31, 57, 31, 115, 415, 445, 557, 3971, 1565, 15223, 7799, 10463, 117387, 225127}}, {21153, 18, 130214, {1, 3, 5, 11, 31, 19, 3, 63, 315, 501, 903, 1925, 3393, 16149, 11013, 15483, 70765, 279}}, {21154, 18, 130228, {1, 3, 3, 9, 29, 21, 13, 227, 263, 815, 1259, 2549, 955, 9237, 16083, 38891, 31145, 731}}, {21155, 18, 130240, {1, 3, 3, 5, 27, 23, 33, 189, 107, 655, 889, 1549, 7315, 13341, 12721, 59339, 54503, 91679}}, {21156, 18, 130267, {1, 3, 7, 5, 15, 9, 1, 255, 451, 91, 1279, 2359, 5913, 5215, 23161, 29327, 45275, 206709}}, {21157, 18, 130280, {1, 3, 3, 9, 9, 41, 75, 91, 87, 695, 335, 3375, 7307, 14095, 5359, 7815, 9339, 46387}}, {21158, 18, 130294, {1, 1, 3, 15, 5, 47, 69, 231, 423, 255, 1335, 3395, 2799, 8955, 31445, 59849, 104955, 240587}}, {21159, 18, 130306, {1, 3, 5, 7, 7, 9, 21, 209, 321, 5, 653, 2199, 3657, 6397, 20229, 32349, 54543, 47971}}, {21160, 18, 130325, {1, 3, 7, 11, 31, 21, 85, 49, 197, 865, 53, 609, 1867, 14503, 12671, 61703, 39245, 8493}}, {21161, 18, 130398, {1, 3, 1, 13, 27, 31, 119, 247, 209, 65, 1729, 1563, 1597, 1617, 26597, 50139, 108667, 77035}}, {21162, 18, 130402, {1, 1, 5, 13, 3, 49, 53, 219, 71, 1013, 1239, 3725, 117, 9273, 8277, 32619, 45933, 71509}}, {21163, 18, 130421, {1, 3, 7, 13, 1, 3, 119, 153, 79, 555, 429, 1221, 3725, 6073, 1295, 7187, 117709, 258911}}, {21164, 18, 130438, {1, 3, 3, 13, 1, 13, 105, 185, 81, 989, 563, 3761, 6725, 4699, 10539, 50247, 95307, 211927}}, {21165, 18, 130441, {1, 3, 7, 3, 21, 11, 45, 81, 495, 391, 1437, 3495, 3789, 13701, 9479, 42505, 22561, 135019}}, {21166, 18, 130475, {1, 3, 3, 11, 7, 61, 65, 211, 269, 997, 385, 3843, 4905, 2939, 28551, 19515, 25177, 68137}}, {21167, 18, 130486, {1, 1, 3, 3, 3, 47, 73, 127, 15, 977, 209, 1791, 4711, 6733, 29093, 36311, 13665, 240603}}, {21168, 18, 130503, {1, 3, 5, 5, 19, 39, 29, 211, 463, 755, 1723, 397, 213, 14009, 22701, 7131, 35587, 183885}}, {21169, 18, 130551, {1, 3, 5, 9, 11, 29, 7, 25, 381, 631, 1343, 2255, 2535, 3239, 7287, 14161, 69295, 85245}}, {21170, 18, 130574, {1, 1, 5, 5, 17, 47, 19, 217, 289, 411, 1855, 323, 4109, 2601, 5835, 61909, 99333, 99959}}, {21171, 18, 130602, {1, 1, 3, 11, 1, 51, 121, 207, 403, 993, 1171, 3451, 3389, 957, 22125, 9333, 110775, 54125}}, {21172, 18, 130612, {1, 3, 5, 15, 9, 51, 13, 251, 203, 861, 321, 2017, 6933, 10785, 20089, 65213, 105451, 117319}}, {21173, 18, 130621, {1, 3, 3, 15, 19, 63, 89, 217, 269, 723, 57, 1923, 4267, 4895, 2191, 21605, 62401, 11063}}, {21174, 18, 130633, {1, 3, 1, 3, 21, 47, 103, 75, 167, 989, 1401, 575, 3717, 10373, 21321, 5487, 36063, 140411}}, {21175, 18, 130684, {1, 1, 7, 15, 19, 29, 121, 197, 429, 773, 901, 1875, 291, 11395, 31459, 55041, 49263, 185143}}, {21176, 18, 130688, {1, 3, 3, 1, 19, 17, 19, 21, 41, 885, 1665, 547, 5887, 6205, 3317, 59399, 125559, 82721}}, {21177, 18, 130698, {1, 3, 1, 9, 15, 39, 81, 9, 279, 33, 1287, 3035, 5759, 10647, 3933, 20953, 3137, 30693}}, {21178, 18, 130700, {1, 3, 5, 13, 3, 33, 33, 169, 233, 83, 467, 3719, 5617, 6165, 15631, 56059, 95541, 245233}}, {21179, 18, 130712, {1, 3, 5, 13, 5, 21, 81, 9, 413, 247, 1307, 3363, 3383, 11525, 1259, 8735, 36507, 98359}}, {21180, 18, 130739, {1, 1, 1, 13, 17, 49, 105, 131, 385, 309, 1295, 565, 8031, 15391, 31263, 52657, 102721, 212195}}, {21181, 18, 130748, {1, 3, 1, 7, 13, 41, 21, 103, 237, 649, 55, 1565, 6327, 8743, 15457, 29975, 34165, 80839}}, {21182, 18, 130774, {1, 3, 5, 11, 15, 31, 121, 219, 375, 159, 731, 59, 3205, 15039, 10023, 46209, 34619, 110253}}, {21183, 18, 130783, {1, 3, 3, 11, 31, 19, 79, 185, 363, 635, 463, 987, 2681, 6405, 30077, 21173, 14213, 58095}}, {21184, 18, 130802, {1, 1, 5, 13, 23, 37, 57, 111, 293, 553, 269, 3393, 345, 1983, 1097, 47217, 22281, 212607}}, {21185, 18, 130811, {1, 3, 5, 7, 7, 33, 65, 61, 185, 411, 187, 641, 6437, 4625, 17547, 38941, 81119, 48651}}, {21186, 18, 130836, {1, 1, 7, 3, 19, 25, 39, 243, 139, 465, 691, 713, 7879, 14539, 31669, 35871, 130681, 255929}}, {21187, 18, 130840, {1, 3, 1, 1, 3, 43, 87, 13, 179, 835, 719, 1189, 7207, 5863, 6077, 20669, 35469, 211155}}, {21188, 18, 130856, {1, 3, 7, 13, 25, 59, 97, 129, 151, 985, 739, 1919, 7729, 14057, 21721, 17603, 82797, 181319}}, {21189, 18, 130864, {1, 1, 7, 7, 5, 3, 21, 141, 379, 257, 207, 597, 4051, 7563, 25481, 59427, 45449, 61159}}, {21190, 18, 130873, {1, 3, 3, 9, 11, 25, 5, 29, 131, 603, 637, 189, 4033, 13099, 15219, 4447, 73501, 135795}}, {21191, 18, 130918, {1, 3, 1, 9, 1, 49, 57, 227, 141, 543, 1499, 3525, 3127, 11191, 4071, 47003, 7431, 155137}}, {21192, 18, 130927, {1, 3, 1, 11, 27, 31, 15, 31, 113, 135, 1251, 245, 6965, 14263, 5679, 55201, 121453, 132503}}, {21193, 18, 130929, {1, 1, 5, 15, 7, 23, 67, 163, 57, 513, 1809, 1343, 6165, 199, 31169, 30803, 86705, 71103}}, {21194, 18, 130958, {1, 1, 3, 1, 15, 9, 75, 143, 273, 797, 819, 4037, 2305, 4841, 15697, 41191, 38187, 174131}}, {21195, 18, 130966, {1, 3, 7, 7, 3, 55, 65, 135, 423, 185, 299, 2221, 7987, 4223, 28183, 32273, 95941, 260297}}, {21196, 18, 130970, {1, 1, 7, 7, 7, 11, 67, 109, 507, 673, 1555, 2537, 7553, 4659, 3945, 20839, 32539, 43053}}, {21197, 18, 130976, {1, 1, 7, 15, 1, 47, 61, 73, 211, 397, 1785, 4063, 6461, 13725, 11299, 17565, 80063, 118271}}, {21198, 18, 131006, {1, 1, 7, 5, 29, 27, 97, 105, 379, 153, 915, 2795, 4933, 6729, 21207, 9995, 70241, 85641}}, {21199, 18, 131008, {1, 3, 5, 5, 23, 13, 41, 67, 127, 649, 1351, 3597, 7077, 4989, 14649, 17401, 70883, 239841}}, {21200, 18, 131020, {1, 1, 5, 1, 19, 1, 83, 3, 425, 873, 1943, 3935, 4257, 14587, 11829, 55217, 21963, 39683}}, {21201, 18, 131059, {1, 1, 7, 11, 15, 7, 37, 239, 337, 245, 1557, 3681, 7357, 9639, 27367, 26869, 114603, 86317}} }; void sobol_generate_direction_vectors(uint vectors[][SOBOL_BITS], int dimensions) { assert(dimensions <= SOBOL_MAX_DIMENSIONS); const uint L = SOBOL_BITS; /* first dimension is exception */ uint *v = vectors[0]; for(uint i = 0; i < L; i++) v[i] = 1 << (31-i); // all m's = 1 for(int dim = 1; dim < dimensions; dim++) { SobolDirectionNumbers *numbers = &SOBOL_NUMBERS[dim-1]; uint s = numbers->s; uint a = numbers->a; uint *m = numbers->m; v = vectors[dim]; if(L <= s) { for(uint i = 0; i < L; i++) v[i] = m[i] << (31-i); } else { for(uint i = 0; i < s; i++) v[i] = m[i] << (31-i); for(uint i = s; i < L; i++) { v[i] = v[i-s] ^ (v[i-s] >> s); for(uint k = 1; k < s; k++) v[i] ^= (((a >> (s-1-k)) & 1) * v[i-k]); } } } } CCL_NAMESPACE_END