---
ext/standard/basic_functions.c | 5 +
ext/standard/mt_rand.c | 67 ++-
ext/standard/php_math.h | 1 +
ext/standard/tests/math/mt_srand_array_basic.phpt | 146 ++++++
ext/standard/tests/math/mt_srand_array_values.phpt | 532 +++++++++++++++++++++
5 files changed, 750 insertions(+), 1 deletion(-)
create mode 100644 ext/standard/tests/math/mt_srand_array_basic.phpt
create mode 100644 ext/standard/tests/math/mt_srand_array_values.phpt
diff --git a/ext/standard/basic_functions.c b/ext/standard/basic_functions.c
index ef628cc..bcceb20 100644
--- a/ext/standard/basic_functions.c
+++ b/ext/standard/basic_functions.c
@@ -1891,6 +1891,10 @@ ZEND_BEGIN_ARG_INFO_EX(arginfo_mt_srand, 0, 0, 0)
ZEND_ARG_INFO(0, mode)
ZEND_END_ARG_INFO()
+ZEND_BEGIN_ARG_INFO(arginfo_mt_srand_array, 0)
+ ZEND_ARG_INFO(0, seed)
+ZEND_END_ARG_INFO()
+
ZEND_BEGIN_ARG_INFO_EX(arginfo_mt_rand, 0, 0, 0)
ZEND_ARG_INFO(0, min)
ZEND_ARG_INFO(0, max)
@@ -2856,6 +2860,7 @@ const zend_function_entry basic_functions[] = { /* {{{ */
PHP_FALIAS(getrandmax, mt_getrandmax,
arginfo_mt_getrandmax)
PHP_FE(mt_rand,
arginfo_mt_rand)
PHP_FE(mt_srand,
arginfo_mt_srand)
+ PHP_FE(mt_srand_array,
arginfo_mt_srand_array)
PHP_FE(mt_getrandmax,
arginfo_mt_getrandmax)
PHP_FE(random_bytes,
arginfo_random_bytes)
diff --git a/ext/standard/mt_rand.c b/ext/standard/mt_rand.c
index dde9a77..04e83dd 100644
--- a/ext/standard/mt_rand.c
+++ b/ext/standard/mt_rand.c
@@ -151,7 +151,10 @@ PHPAPI void php_mt_srand(uint32_t seed)
{
/* Seed the generator with a simple uint32 */
php_mt_initialize(seed, BG(state));
- php_mt_reload();
+
+ /* Reload the generator when mt_rand is next called.
+ * (Reloading immediately would break php_mt_srand_array.) */
+ BG(left) = 0;
/* Seed only once */
BG(mt_rand_is_seeded) = 1;
@@ -209,6 +212,68 @@ PHP_FUNCTION(mt_srand)
}
/* }}} */
+/* {{{ proto void mt_srand_array(array seed)
+ Seeds Mersenne Twister random number generator with multiple integers */
+PHP_FUNCTION(mt_srand_array)
+{
+ zval* arr = 0;
+ zval* tmp;
+ uint32_t length = 0, seed_j;
+ int i, j, k, first_loop = 1;
+ uint32_t* mt = BG(state);
+
+ if (zend_parse_parameters(ZEND_NUM_ARGS(), "a", &arr) == FAILURE)
+ return;
+
+ length = zend_hash_num_elements(Z_ARRVAL_P(arr));
+ if (length == 0) {
+ php_error_docref(NULL, E_WARNING, "Argument must be an array
with at least 1 element");
+ return;
+ }
+
+ ZEND_HASH_FOREACH_VAL(Z_ARRVAL_P(arr), tmp) {
+ if (Z_TYPE_P(tmp) != IS_LONG) {
+ php_error_docref(NULL, E_WARNING, "Argument must be an
array with only integer elements");
+ return;
+ }
+ if (Z_LVAL_P(tmp) > 0xffffffffU) {
+ php_error_docref(NULL, E_WARNING, "Seed values will be
truncated at 32 bits");
+ return;
+ }
+ } ZEND_HASH_FOREACH_END();
+
+ php_mt_srand(19650218U);
+ i = 1;
+ k = 0;
+ while (k < N) {
+ j = 0;
+ ZEND_HASH_FOREACH_VAL(Z_ARRVAL_P(arr), tmp) {
+ seed_j = Z_LVAL_P(tmp);
+ mt[i] = ((mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) *
1664525U)) + seed_j + j) & 0xffffffffU;
+ i++; j++; k++;
+ if (i == N) {
+ mt[0] = mt[N-1];
+ i = 1;
+ }
+ if (!first_loop && k == N) {
+ break;
+ }
+ } ZEND_HASH_FOREACH_END();
+ first_loop = 0;
+ }
+ for (k = 1; k < N; ++k) {
+ mt[i] = ((mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941U))
- i) & 0xffffffffU;
+ i++;
+ if (i == N) {
+ mt[0] = mt[N-1];
+ i = 1;
+ }
+ }
+
+ mt[0] = 0x80000000UL;
+}
+/* }}} */
+
/* {{{ php_mt_rand_range
*/
PHPAPI zend_long php_mt_rand_range(zend_long min, zend_long max)
diff --git a/ext/standard/php_math.h b/ext/standard/php_math.h
index 3ff0f04..0eaf34c 100644
--- a/ext/standard/php_math.h
+++ b/ext/standard/php_math.h
@@ -48,6 +48,7 @@ PHP_FUNCTION(pow);
PHP_FUNCTION(sqrt);
PHP_FUNCTION(rand);
PHP_FUNCTION(mt_srand);
+PHP_FUNCTION(mt_srand_array);
PHP_FUNCTION(mt_rand);
PHP_FUNCTION(mt_getrandmax);
PHP_FUNCTION(abs);
diff --git a/ext/standard/tests/math/mt_srand_array_basic.phpt
b/ext/standard/tests/math/mt_srand_array_basic.phpt
new file mode 100644
index 0000000..9632ff6
--- /dev/null
+++ b/ext/standard/tests/math/mt_srand_array_basic.phpt
@@ -0,0 +1,146 @@
+--TEST--
+Test mt_srand_array() - basic function mt_srand_array()
+--FILE--
+<?php
+
+// Should produce the same mt_rand output with the same seed.
+mt_srand_array([1,2,3,4,5]);
+$a = [mt_rand(), mt_rand(), mt_rand(), mt_rand(), mt_rand(), mt_rand()];
+mt_srand_array([1,2,3,4,5]);
+$b = [mt_rand(), mt_rand(), mt_rand(), mt_rand(), mt_rand(), mt_rand()];
+var_dump($a == $b);
+
+// Should produce different mt_rand output with a different seed.
+mt_srand_array([1,2,3,4,6]);
+$c = [mt_rand(), mt_rand(), mt_rand(), mt_rand(), mt_rand(), mt_rand()];
+var_dump($a == $c);
+
+// Should return NULL if the argument is an array of integers.
+var_dump(mt_srand_array([1]));
+var_dump(mt_srand_array([1, 2]));
+var_dump(mt_srand_array([1, 2, 3]));
+
+// Should give warnings if the argument is not an array of integers.
+var_dump(mt_srand_array());
+var_dump(mt_srand_array(NULL));
+var_dump(mt_srand_array(true));
+var_dump(mt_srand_array(false));
+var_dump(mt_srand_array(1));
+var_dump(mt_srand_array(1.2));
+var_dump(mt_srand_array('x'));
+var_dump(mt_srand_array([]));
+
+var_dump(mt_srand_array([NULL]));
+var_dump(mt_srand_array([true]));
+var_dump(mt_srand_array([false]));
+var_dump(mt_srand_array([1.2]));
+var_dump(mt_srand_array(['x']));
+
+var_dump(mt_srand_array([1, NULL]));
+var_dump(mt_srand_array([1, true]));
+var_dump(mt_srand_array([1, false]));
+var_dump(mt_srand_array([1, 1.2]));
+var_dump(mt_srand_array([1, 'x']));
+
+var_dump(mt_srand_array([NULL, 1]));
+var_dump(mt_srand_array([true, 1]));
+var_dump(mt_srand_array([false, 1]));
+var_dump(mt_srand_array([1.2, 1]));
+var_dump(mt_srand_array(['x', 1]));
+
+var_dump(mt_srand_array([NULL, NULL]));
+var_dump(mt_srand_array([true, true]));
+var_dump(mt_srand_array([false, false]));
+var_dump(mt_srand_array([1.2, 1.2]));
+var_dump(mt_srand_array(['x', 'x']));
+?>
+--EXPECTF--
+bool(true)
+bool(false)
+NULL
+NULL
+NULL
+
+Warning: mt_srand_array() expects exactly 1 parameter, 0 given in %s on line %d
+NULL
+
+Warning: mt_srand_array() expects parameter 1 to be array, null given in %s on
line %d
+NULL
+
+Warning: mt_srand_array() expects parameter 1 to be array, boolean given in %s
on line %d
+NULL
+
+Warning: mt_srand_array() expects parameter 1 to be array, boolean given in %s
on line %d
+NULL
+
+Warning: mt_srand_array() expects parameter 1 to be array, integer given in %s
on line %d
+NULL
+
+Warning: mt_srand_array() expects parameter 1 to be array, float given in %s
on line %d
+NULL
+
+Warning: mt_srand_array() expects parameter 1 to be array, string given in %s
on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with at least 1 element
in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
+
+Warning: mt_srand_array(): Argument must be an array with only integer
elements in %s on line %d
+NULL
diff --git a/ext/standard/tests/math/mt_srand_array_values.phpt
b/ext/standard/tests/math/mt_srand_array_values.phpt
new file mode 100644
index 0000000..267087b
--- /dev/null
+++ b/ext/standard/tests/math/mt_srand_array_values.phpt
@@ -0,0 +1,532 @@
+--TEST--
+Test mt_srand_array() - check compability with init_by_array in mt19937ar.c
+--FILE--
+<?php
+// This seed data has been generated with mt_rand.
+// The result of this test has been verified with the
+// init_by_array() function as implemented in mt19937ar.c,
+// www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/CODES/mt19937ar.c
+// Retrieved on 2016-08-14.
+$init = [
+533797649, 477972911, 238644764, 2053609391, 2114488238, 1672166357,
+1677789847, 113814253, 405100136, 1295645083, 1280130337, 1621368104,
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+886805278, 569348619, 710948850, 634958263, 1429967020, 882231681,
+1937446023, 1982659960, 36274821, 1191994465, 1300109346, 1618746190,
+1396450738, 362665554, 302920921, 135629471, 357568549, 1648999768,
+661482772, 2114789554, 697545551, 1867848860, 1050863912, 1865143872,
+1475217165, 830960919, 1447789791, 1185255739, 502046053, 1123548340,
+1055621189, 1618672631, 2041212379, 109892516, 1227019944, 1854791485,
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+810810644, 1168805588, 898359224, 629482809, 2120956570, 1069280196,
+1511095111, 2087090462, 225047305, 1637362290, 308575013, 1352330332,
+734850344, 670808293, 178357535, 594394980, 1139434567, 883284580,
+1397948317, 28912352, 1446748190, 617861994, 815347173, 1963980261,
+214445682, 907035403, 1143999893, 2062970592, 1984051944, 1774362025,
+512798853, 702140750, 1001106098, 46214571, 1156971972, 1201543040,
+1503090317, 1780990882, 835930457, 884260311, 901771492, 422424056,
+1503069960, 705444497, 578874916, 1062852456, 894989764, 899631711,
+370578589, 1202931154, 383520217, 1327620695, 1831710089, 1086004548,
+1255965593, 840271333, 115928733, 577490500, 78584127, 727056064,
+1752936049, 964887523, 1154711175, 1071664748, 1480358451, 203805324,
+1469054064, 1290874799, 269418577, 1171314433, 215271957, 370094284,
+968856636, 1657607566, 1042793512, 2015382843, 383027214, 1758820919,
+344860887, 647079493, 876643877, 2101300674, 987426396, 16729551,
+1784043767, 1572338717, 843065412, 2067471506, 1502869217, 1799646693,
+213285071, 377052203, 1830446282, 982272583, 414733416, 410793732,
+873346518, 503246214, 797656459, 628299992, 512241280, 948656140,
+1451451600, 345895028, 518757933, 1588415604, 984200527, 1086753412,
+544527639, 874200561, 1470690041, 484206177, 909376930, 1486600433,
+1937975887, 559677004, 1994302069, 823577794, 1116225413, 1743029005,
+1827892021, 1879629231, 423581839, 541026028, 494758223, 1435770877,
+1598155535, 1964981539, 329093792, 1832472320, 1087574585, 1101854573,
+1378007344, 1228236959, 1945133695, 646893932, 1415173992, 1529640465,
+2079401260, 780838700, 1293285469, 391785176, 677753081, 15747793,
+1894718671, 1670274714, 1046250815, 448209684, 335857912, 1765225040,
+1801777069, 527995858, 1721154109, 749717364, 1565144236, 1819753500,
+8884840, 1129870710, 243516099, 2113571701, 1846885628, 940241410,
+1962405398, 190731176, 2008927995, 1226017471, 1368340416, 1104933192,
+1064493189, 218937022, 297879713, 320860513, 818032854, 1949568466,
+314939544, 1795587253, 175992163, 1319391772, 1174222140, 1170802330,
+1061966846, 71721662, 762971128, 182330249, 299574656, 469546625,
+761501604, 53300548, 188294742, 673141118, 648693521, 382299026,
+1870609055, 466728501, 943212212, 1609815508, 262702628, 1507117809,
+161574838, 1019440860, 2050064521, 1425857550, 1492014039, 944287347,
+1007097370, 1757596940, 2090286765, 1730912181, 1320997748, 1589615122,
+1451147491, 1108660228, 2020426077, 892328452, 1655953465, 43749229,
+1376485909, 1317737148, 1415607683, 1841115553, 1460021946, 1886464852,
+1408187472, 154974876, 1191879427, 77435359, 192555798, 595802156,
+920350281, 436095593, 1462774350, 655206373, 1051033499, 752363624,
+1787149375, 595615018, 1665287633, 1590146048, 1769673860, 340684559,
+1652562876, 1824116798, 475024620, 2086628846, 880062478, 256075702,
+340587598, 290281509, 584831433, 2007516777, 1343890550, 349845801,
+1336747094, 568610678, 61799944, 236329154, 526799089, 506356879,
+1740532421, 1879730506, 1990728978, 1915293831, 938595895, 1825498368,
+494032435, 1757730800, 2044538616, 1112573724, 624804594, 1321575931,
+1948102067, 1208497950, 698867660, 1730012823
+];
+
+printf("init %d\n", 5);
+mt_srand_array(array_slice($init, 0, 5));
+for ($i = 0; $i < 1000; ++$i) {
+ if ($i) echo ($i % 6 == 0 ? "\n" : " ");
+ printf("%d,", mt_rand());
+}
+echo "\n";
+
+printf("init %d\n", count($init));
+mt_srand_array($init);
+for ($i = 0; $i < 1000; ++$i) {
+ if ($i) echo ($i % 6 == 0 ? "\n" : " ");
+ printf("%d,", mt_rand());
+}
+echo "\n";
+?>
+--EXPECT--
+init 5
+1678085969, 173170251, 1782802870, 937957818, 2049075857, 475493648,
+631159003, 265551473, 367318037, 180728820, 882767285, 518593020,
+1483604447, 134774193, 964352505, 1672651821, 88387593, 624398452,
+768905273, 62945995, 1786727054, 129379898, 1251426231, 120487373,
+1588634830, 646438254, 2062420793, 624611897, 380598150, 1999644287,
+126446955, 159634314, 1420847270, 727488664, 299098148, 414993981,
+987722467, 1753145380, 1045592542, 12767669, 1223761434, 1813465931,
+171025115, 335674505, 1777844237, 2046360196, 549508484, 2060432233,
+1478591136, 82598413, 1437272609, 188008750, 537318096, 1563000981,
+1322768027, 122924280, 989201561, 1838053780, 1524406237, 402767818,
+1357934275, 518154174, 1970896318, 1291492803, 1703288044, 1710090268,
+1134974040, 1205530280, 1564219437, 1959999115, 2070873944, 1093246373,
+1774468942, 1548462422, 1537766937, 2470930, 1730334238, 542124953,
+1485726082, 1611191139, 1615506211, 1744134923, 1032166749, 373825211,
+1185635659, 2054543400, 1408272743, 222902069, 934971869, 325709765,
+1848019873, 1701075729, 390124953, 773120821, 360567826, 1789065666,
+1134188761, 235988203, 1649775550, 1866268786, 1865237225, 308439968,
+488266067, 671018254, 112438428, 495480977, 1667523297, 584455950,
+1606364015, 803240708, 681841472, 1884613027, 879967411, 1244875426,
+1958303277, 1169798427, 2067773861, 399232754, 429408626, 1444908741,
+1397404058, 438083513, 51005745, 677540897, 1848792993, 2040283834,
+73877667, 641558522, 210465773, 670213318, 1962329747, 213848257,
+127734689, 1159679712, 309719363, 343863574, 451160292, 363285968,
+920300268, 1223618319, 2092752885, 716753896, 253388247, 1033700545,
+656469891, 964333406, 626675494, 668764599, 284541113, 716974699,
+1552757841, 2122977183, 1961264786, 159796457, 954597579, 76987656,
+458685897, 745258981, 1725018277, 222533039, 811460418, 247922055,
+421883548, 381762822, 756499932, 942630902, 1560631298, 772857810,
+1894117589, 733999678, 793502595, 1322008488, 1614401720, 1495641839,
+1158576564, 1823434050, 1664573103, 7566840, 1727024249, 798041803,
+582370562, 304218954, 838981650, 314510836, 1828785517, 1104865992,
+426047409, 254634264, 1052462887, 654559757, 1110467271, 1368997850,
+1332370983, 1298526292, 1717151294, 1299785270, 1205967042, 1945591610,
+39245245, 252233892, 1379438881, 1563554062, 55749522, 1281643592,
+772214558, 419402223, 2139436058, 1438909276, 116548681, 977950774,
+1843696587, 262197124, 1027335544, 99463235, 1377044058, 272767630,
+2076200847, 785296613, 1095742480, 1187187832, 476552792, 834384586,
+140321133, 1895093493, 1704339120, 1206230228, 672749714, 701573697,
+712587138, 559763958, 1833886670, 1246194772, 131970736, 1026960167,
+258531498, 533309357, 302809735, 78705794, 180401783, 1438221774,
+1171710223, 62233318, 1114313937, 181783356, 1372495881, 1525021015,
+1081472076, 863314220, 1154718358, 632560915, 447829343, 172268965,
+892950544, 638504668, 1927157561, 48066633, 1048890682, 1639383707,
+214700437, 2091128935, 1398268525, 2787833, 404111919, 1496088284,
+1568785210, 1237637766, 2024715775, 1070278879, 333332389, 222404898,
+530985834, 436107194, 898494426, 2002031102, 1463945304, 1047357225,
+877606586, 1779966837, 777777644, 2047233898, 1397786520, 1397326652,
+1888920804, 1987775265, 1343238365, 1521274607, 1664471951, 1824675909,
+1214837658, 687267230, 1318012059, 1523568963, 1569744542, 2040235203,
+1458478110, 813839624, 516195500, 1706443716, 387069934, 826717497,
+661029222, 1698099585, 1619086966, 472920484, 397208282, 1546010573,
+1459811472, 155769548, 1005470241, 1332622415, 1401701839, 929943807,
+17496501, 167865207, 39119769, 1549803902, 1275144214, 402453424,
+291332047, 119011701, 424791945, 1635111346, 1008471199, 1235519240,
+1964241044, 1171691282, 407274744, 264819878, 2127954766, 936159281,
+1125822853, 1147029717, 656833846, 1991402116, 1226342161, 1812321691,
+524992088, 1810773922, 2026071844, 1615449650, 2126358431, 270824574,
+272446342, 1116242880, 1796886580, 697118066, 1732398470, 134944144,
+396856570, 1781884880, 2062414019, 102202061, 614318803, 2073719717,
+42103060, 1524008207, 1003551051, 1324347014, 343150315, 121854185,
+1749758390, 2086808537, 1267592318, 72062746, 1207296988, 1643045338,
+165847348, 965850327, 1630973577, 1485469182, 306799380, 643908446,
+735844106, 613194827, 1424491263, 20870783, 1683414788, 814852722,
+1645422996, 1591969802, 108681618, 596735742, 581347169, 238372006,
+2057427754, 411896601, 179840892, 1171842900, 1243785904, 1160793500,
+1168001476, 1701651494, 1573335512, 919745851, 1423498746, 1599105340,
+59486933, 1946207583, 255480857, 230755676, 582759138, 1782505704,
+1014623654, 93567142, 501546608, 445395111, 1698508681, 2118306626,
+2044371843, 1590884942, 1855172077, 2132429415, 693554267, 1540348537,
+1524008423, 1598749681, 1162339897, 83169613, 1582659019, 1386408935,
+452518407, 399739662, 562081531, 1749652889, 456329004, 1651421807,
+417441467, 72768787, 188189810, 938986731, 1267364468, 1263903786,
+943353794, 831740732, 573154911, 930464617, 1706902055, 320044701,
+1848930605, 759699675, 650016838, 603605656, 1295110101, 1682265851,
+548352407, 1646100528, 1470310168, 1395219556, 2057341385, 1454271902,
+1152371462, 287938688, 1313390732, 732216538, 1611562077, 2108866735,
+1791254179, 1695098182, 860924454, 1071154156, 1595681364, 1110578611,
+967111431, 529535867, 1747680551, 1901288299, 1146121481, 1032369048,
+1561952783, 281435437, 1575636635, 709983939, 1682585696, 792937343,
+706127520, 1356220838, 1323583891, 741089452, 1871351301, 296217876,
+1643734231, 206775477, 1705966924, 948141888, 1049519578, 739897487,
+125778627, 112303069, 864415289, 542025605, 667129468, 965667788,
+2070292383, 631287150, 173144548, 1697432442, 996099145, 604261523,
+1447892832, 837818285, 445235679, 1499594811, 876824624, 393233787,
+1626380339, 1303856788, 855369858, 188641682, 1681158451, 2094210553,
+1781204178, 1135663622, 704285652, 1880224068, 425221731, 327473624,
+1039642257, 1565338083, 414946522, 1010064589, 1264913340, 1515349606,
+1511659415, 867897001, 424884116, 187908546, 2064028594, 1318843210,
+1200326261, 1171921289, 1755282560, 577579416, 1963270104, 108604668,
+1465657995, 2134994058, 54063649, 1922385414, 2134814091, 920509373,
+1371241837, 179734609, 1753977750, 1881176241, 1160194538, 633203641,
+248257266, 160432164, 1174083751, 1869649959, 1265733541, 342753628,
+1042343179, 1558817004, 662228230, 426303967, 52599397, 417304543,
+563481354, 1959363161, 1012360589, 1480861398, 1091180077, 757484865,
+402810392, 22659448, 2104312645, 1393473726, 313079060, 1720345614,
+1547286608, 440350497, 1038702504, 1320656001, 139557658, 160814655,
+1120448208, 1630894778, 1823854524, 2112880666, 254049795, 769182217,
+1988273240, 265535314, 155513257, 910763639, 1494357430, 336664448,
+709382536, 1371967891, 460724405, 1851926075, 1543123287, 1951024034,
+757250103, 371934696, 1711929196, 1140185691, 1916650934, 763374904,
+1270790180, 1862915836, 1428366502, 224431428, 1025831708, 1353196886,
+1472340786, 617723365, 1667847487, 2145832122, 499682359, 1225554127,
+879776645, 1531037326, 1162895834, 317423246, 1685725841, 726301581,
+1445098093, 1518570230, 207578906, 1570892321, 507703530, 1028678219,
+1908778501, 251699072, 803730769, 1725031729, 1231638911, 184249436,
+1657312598, 182416268, 659889559, 1076854276, 1227109276, 2101310460,
+1080262363, 2010944041, 872294238, 296576621, 1639843353, 1055468010,
+1221834574, 1640475125, 1586738399, 1885305952, 183220722, 498344677,
+444321987, 1643254950, 1707056411, 840347155, 701891000, 1586612615,
+2069168262, 146270803, 833420350, 493189987, 773262803, 1653658434,
+2052935862, 1732568101, 589336318, 1317029499, 1947842396, 1625044604,
+2067190720, 1938660402, 2127461260, 1833473329, 1769289178, 675228003,
+1274493809, 2030117365, 2111336557, 889705256, 1313670825, 978867720,
+1124383289, 1081615542, 872995886, 1580286787, 1743304828, 2065619306,
+141336252, 900473833, 1276311040, 1031012968, 1684506321, 1715923687,
+113051291, 2103905761, 1796447328, 1481419947, 1265353271, 463463765,
+1181842726, 1864289951, 1391445669, 1561920507, 1690657304, 539450648,
+233976639, 1781460989, 102116313, 277501659, 2057695232, 399374154,
+253291389, 213054850, 1549165702, 141993661, 609980912, 954361616,
+369994966, 1963169244, 1461655693, 1456507482, 559744717, 584737195,
+1489543623, 559564535, 140274584, 970099295, 392790864, 54182867,
+593868692, 2140733955, 101159131, 2024047281, 1266096579, 606195139,
+1602404067, 2060457720, 1761718118, 1836011858, 785892683, 1716308014,
+861070048, 1702443877, 941622984, 378366524, 152594682, 167909708,
+314963998, 630854539, 1798994002, 1389044097, 985097841, 1157040721,
+265075438, 1429980301, 499489890, 623159753, 1172125800, 886466981,
+183494643, 564774918, 1898626953, 306976580, 810859339, 291570861,
+1487607786, 1852587929, 2013416964, 214002840, 1133515065, 729846310,
+2122565116, 1966058439, 1973273434, 906557283, 1982866876, 1725046252,
+922159523, 1680009188, 636183905, 492096369, 1065504721, 1658221372,
+1915213760, 20704986, 2054518307, 417623390, 338259801, 1772577704,
+1164295913, 1487400349, 1198936352, 941802882, 710953151, 41436756,
+694551391, 1780791007, 1670172407, 510226143, 1704983228, 1234576800,
+2017484910, 1987089499, 877072623, 218656974, 1882899491, 203698556,
+1513215802, 1080859235, 722664779, 663232474, 694739582, 37157761,
+321239494, 1340305956, 569186972, 1999156701, 1125628319, 2053000467,
+931556325, 1339953903, 474370210, 1778883985, 27178352, 1364274459,
+2116793083, 1332866977, 451364122, 277350424, 1259803477, 806709477,
+710988522, 568129536, 1525314388, 1589055462, 1649655838, 24851681,
+1191362823, 652466018, 51507135, 1949811523, 1420215882, 20117642,
+1857490136, 612776782, 848703729, 212984899, 488209359, 894858669,
+749747098, 1449304251, 1395664211, 1033532758, 2065110276, 1559613251,
+265952038, 943542317, 1998024290, 313914991, 1194859837, 389750550,
+411229008, 840806755, 292338179, 1161175231, 317219581, 507864395,
+606806965, 1325384287, 955404346, 1246677080, 1322281139, 1598537319,
+1166023292, 1450778928, 1637022860, 731667986, 2073782484, 1004998191,
+102564534, 815125906, 1576098225, 1524965501, 5313864, 1823974573,
+1773504912, 1041743912, 881554341, 960776758, 552712693, 408302745,
+2114071279, 992220049, 511892365, 1697239197, 1629776795, 1137469311,
+576094438, 427212158, 202025744, 1805447936, 542712707, 1212058647,
+1131832821, 691738312, 1352812628, 892381556, 715334465, 1341375748,
+564271455, 1911559160, 1475034391, 158936189, 2098991028, 1661681153,
+988209962, 1208631994, 1931293838, 1520770876, 1957491147, 1319211690,
+1839734598, 98025503, 1898820039, 191381922, 1071988827, 346778027,
+2076473163, 1923156889, 42870090, 904787726, 371487994, 1174099381,
+2065179007, 1990282685, 2063040778, 837926979, 2070802548, 1660082840,
+1062920547, 383910317, 240858277, 1821874888, 578052854, 1794193445,
+840412869, 1649530704, 327206201, 856874774, 452646903, 256085065,
+1309181648, 92993917, 1316491931, 226414572, 1946863354, 2098432716,
+590780777, 775622219, 65186292, 312039255, 499083469, 300853689,
+85727687, 423103458, 1603448541, 260765600, 654212345, 1927590285,
+829298165, 1361679699, 1252981468, 925948379, 1531851382, 1392425081,
+1592767896, 2055439648, 726498016, 1752842652, 660098655, 361867427,
+1775381738, 660450687, 1118322932, 87583662, 880921452, 25581819,
+61209221, 1474069918, 1248142062, 1390035608, 241286489, 2001493941,
+1791774504, 709352275, 801736976, 1302784851, 876575406, 827516598,
+850464784, 1956581916, 378456154, 2036444036,
+init 1000
+1566269010, 1577817406, 983081823, 466847167, 1269997621, 1570102927,
+1175203448, 387128547, 1152641261, 1675164555, 708054521, 809195642,
+1154980224, 893776526, 1466993235, 1987264596, 1777519094, 1792057342,
+1900130956, 212087530, 1214906941, 1386095814, 481453987, 572437858,
+685038779, 556063355, 113351045, 1147151342, 1609864850, 1641590377,
+440937637, 1789685137, 458387830, 1071903074, 1137640085, 499179440,
+1927787531, 91245143, 204426269, 508877080, 625409662, 745281164,
+599264206, 22418560, 1714492083, 2145982767, 686507795, 1893975320,
+862119871, 199956756, 1333019389, 535957904, 645851752, 714371650,
+1604067957, 974054946, 1803085920, 413150636, 709122057, 1006236295,
+2072315812, 1641026853, 2116076672, 1963131314, 2015575705, 1754791675,
+1596226318, 1376496955, 402027722, 718707965, 1312024918, 157830053,
+860495892, 1684103858, 2096376248, 2087857649, 969316396, 344059322,
+2098340507, 907491929, 54656404, 1846526534, 572433124, 1476099654,
+1952268768, 1336999301, 815101974, 507852672, 623075903, 1602813023,
+1112061737, 1788404453, 1706235013, 1830416895, 130726061, 1202957358,
+1905013405, 17696991, 803084719, 1542037857, 1753073656, 553315491,
+1037031163, 413050390, 1972842238, 490076427, 768679251, 2032313061,
+1900005591, 1909296309, 1630406245, 338865021, 258597916, 1567660738,
+1886914963, 37364240, 96683127, 815918524, 1278067042, 3952756,
+720030699, 1872939470, 2030750901, 417006013, 971097311, 256405565,
+454406216, 2143061063, 2080327435, 1110617569, 1518651660, 608778944,
+1773476245, 436639808, 412565702, 2122330027, 813463571, 189556107,
+42983345, 252282741, 750734589, 1836585880, 1849636644, 1128503777,
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--
2.9.3
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