Statistics

Problem Statement for "RepeatedHalving"

Problem Statement

You have a collection of bags, each containing some marbles. You are given the int[] bags that describes this collection: each element of bags is the number of marbles in one of the bags.

Consider the following process:

  1. Find the bag that currently contains the most marbles. (If there are several bags tied for having the maximum number of marbles, pick any one of them.)
  2. Remove half of the marbles from that bag. Round the number of removed marbles up if necessary. (E.g., if there are 21 marbles in the bag, you remove 11 and leave 10 in the bag.)
  3. Throw away the removed marbles.

You are going to repeat the above process steps times.

Determine the final numbers of marbles in the bags. Return a int[] containing these numbers sorted in non-descending order.

Definition

Class:
RepeatedHalving
Method:
simulate
Parameters:
int[], int
Returns:
int[]
Method signature:
int[] simulate(int[] bags, int steps)
(be sure your method is public)

Constraints

  • bags will contain between 1 and 100 elements, inclusive.
  • Each element of bags will be between 0 and 10^9, inclusive.
  • steps will be between 1 and 10^9, inclusive.

Examples

  1. {1, 2, 3, 21, 5, 4}

    4

    Returns: {1, 2, 2, 2, 3, 4 }

    We select the bag with 21 marbles and remove 11 of them, leaving 10. We select the bag with 10 marbles and remove 5 of them, leaving 5. We select either one of the two bags with 5 marbles and remove 3 of them, leaving 2 in that bag. We select the other bag with 5 marbles (which is now the only bag with that many marbles) and we remove 3 of them, leaving 2. Remember that the return value must be sorted. E.g., the array {1, 2, 3, 2, 2, 4} has the correct pile sizes but not in the correct order, and thus it would not be accepted as an answer.

  2. {1, 1, 1, 1, 1}

    5

    Returns: {0, 0, 0, 0, 0 }

    In each step we select a different bag and we remove the one marble it contains.

  3. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

    1000000000

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    In each step we select an arbitrary bag and we remove half of the marbles it contains. (I.e., we remove zero marbles and keep zero marbles in the bag.) Keep in mind that a straightforward simulation of 10^9 steps, one at a time, will take quite a lot of time to complete.

  4. {123, 4568, 89123, 45, 678901234}

    27

    Returns: {45, 123, 1142, 1294, 1392 }

  5. {1000000000}

    29

    Returns: {1 }

  6. {1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000}

    2999

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 }

  7. {3, 124999, 221110, 226, 2215, 30820839, 1098194, 646882043, 0, 251, 4270940, 437859851, 243190, 94, 56300, 12157, 1, 3579639, 441405, 91223, 68, 13, 6, 231624, 49337, 5, 448211479, 62, 5118273, 15379007, 447243, 1649029, 198369226, 25554709, 1106, 26614, 234744, 184, 321879, 741433, 4036, 166, 8440, 18, 3, 63996}

    492537040

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  8. {1, 260868267, 437546065, 35046489, 194778, 54, 5603, 31, 375099066, 9, 13, 58481, 6, 8199, 652608, 4646, 1066, 138, 10, 8312970, 63, 62494, 133690, 2406882, 20, 450081763, 573241, 197166181, 2353990, 2552, 0, 3, 1, 83, 101339, 304455, 259851, 565, 659916619, 7517, 1644, 259327, 335361, 2, 258037518, 1000096, 34754188, 4638, 26428444, 33225674, 40247, 12501034, 1702, 30, 0, 156810, 2012154, 134, 740114549, 52818346, 1, 128802, 2328, 5108953, 262346951, 112979, 212781, 5774, 4961404, 647123402, 52756, 3410, 112737, 81711621, 39807665, 124302619, 1126, 1139, 478812306, 805215, 181, 363, 13099, 15408, 568, 15, 0, 0, 7843, 61464, 397264, 308, 319, 359568159, 6853, 30343, 788671856, 50010}

    695702143

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  9. {472081694, 129094111, 356253}

    974553094

    Returns: {0, 0, 0 }

  10. {21, 303003, 29852, 1, 11074, 482052687}

    80

    Returns: {0, 0, 0, 1, 1, 1 }

  11. {4804879, 116537, 0, 4093, 8012159, 915616, 5221776, 59014, 4, 30879824, 4950, 90574277, 268050433, 30777, 311282, 3389, 5706, 918}

    68

    Returns: {0, 4, 918, 3389, 4093, 4950, 5706, 22112, 28613, 29134, 29507, 30156, 30777, 31297, 32721, 37538, 38910, 40795 }

  12. {27297, 634223, 252, 19888029, 1084, 2381, 379709, 46581, 49655, 3383016, 40221, 301962304, 346, 24291, 3989, 0, 235819, 385483, 916560, 20357974, 577, 19, 87, 2, 43787, 5581861, 2, 14, 113858575, 7, 368, 1776112, 9900238, 853703, 4, 40, 891428482, 317233514, 54984225, 15585482, 55846, 31054619, 984740, 7480, 8310258, 0, 52, 1, 161359710, 10224, 6, 4579, 703, 487894402, 31948, 2598462, 391614824, 33, 130229, 657, 1392131, 13238476, 2, 6699986, 1, 216, 185817706, 93724, 1783, 11, 280252, 26897538, 419212, 5003, 7522, 2043, 812633489, 1, 98, 2287, 70330243, 2829, 15389830, 1205, 1718, 9302, 151788157, 25126, 2, 46, 495047794, 22854}

    106376815

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  13. {268363, 182, 114382, 23404, 922, 289016394, 1918307, 864, 136226108, 4, 280, 376792, 33779967, 1, 3948}

    23

    Returns: {1, 4, 182, 280, 864, 922, 3948, 23404, 114382, 268363, 376792, 532133, 564485, 959153, 1055623 }

  14. {961460333, 55565, 1, 415, 1, 14856, 6984477, 4948705, 235, 1225, 3680048, 2770, 271, 0, 181243, 11, 2, 7599, 7561, 164516, 14, 125839, 165, 2, 194372, 42162297, 2, 9, 41109, 415296, 240731, 129508, 274443, 20, 392575084, 82850349}

    459

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

  15. {516071, 265765090, 13258, 7780, 358341, 0, 8088, 29754, 895, 105105, 27088480, 3590, 1, 15, 2463, 40778320, 139971, 1720, 1357890, 0, 217, 17, 30612309, 26983, 12, 811915291, 930, 1282486, 43, 383000, 419917106, 1563839, 13777, 352226343, 924435646, 5, 363846613}

    553

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }

  16. {27527841, 740238, 25138065, 580680593, 1803, 180371836, 21963, 372214448, 2267, 27092, 75320, 152, 11, 227, 82005619, 219, 7, 1484, 384, 881345690, 141119, 11869171, 484, 13844616, 10304874, 10, 204127119, 792, 6, 34, 12927680, 375945, 63, 18921, 2143, 681472, 7, 368, 122681206, 11572765, 2, 758654, 77237, 120492, 417, 1267, 3, 11663, 10359329, 615138, 110187, 16513003, 24123310, 1, 450, 143, 3, 11800, 64575, 419, 6134, 434424, 186051, 90928320, 47, 9084991, 0, 3189925, 6666400, 187517482, 856, 44159, 6943923, 1402}

    1011

    Returns: {0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 }

  17. {1, 15565, 304, 33296648, 25852988, 801, 3007285, 62242496, 3, 462712}

    593608953

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  18. {23, 27, 103, 1, 4083845, 0, 1042, 822489, 234, 12349177, 15634, 1, 5285914, 7569861, 11258, 69, 3900, 78605, 69008, 124302, 129170, 44375665, 23, 209, 63, 50773, 12376, 631, 774012590, 12653955, 24360318, 1, 121, 4905416, 733, 608, 25509617, 43062}

    487453591

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  19. {5575301, 2, 37298731, 91208529, 315974, 277, 27533566, 18, 12710, 6, 63, 337639, 10674647, 94, 425974, 244, 17659385, 352}

    221

    Returns: {2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6 }

  20. {252, 60, 0, 1530, 2781, 22695393, 17, 52, 473217, 838741, 6439370, 621633, 373, 1, 432740643, 101, 64188134, 21, 105219, 32217379, 405, 289292, 54134919}

    36

    Returns: {0, 1, 17, 21, 52, 60, 101, 252, 373, 405, 1530, 2781, 105219, 289292, 473217, 501469, 503396, 621633, 709231, 804921, 838741, 845196, 845858 }

  21. {471695, 242479, 14, 2966, 59871, 3963473, 89443, 230, 855, 167675916, 3831, 9, 7831989, 94, 0, 134, 28087148, 3288, 2927688, 145, 1154747, 86, 446999, 1195, 2095437, 199, 14562747, 35, 51032612, 24011, 1277920, 52799, 28, 179, 51135, 11080419, 26, 12, 19618, 389, 14, 1508578, 86, 3, 42319, 64768911, 13341241, 1, 193507664, 38, 63, 3286, 3168128, 0, 112127940, 1884, 4, 890763537, 408053888, 95910, 167179, 127, 91834, 8960925, 5601165, 0, 213317, 110, 97854331, 126, 1437, 62053660, 30, 378781, 1, 11990, 4244, 4636, 22720}

    301346481

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  22. {0, 127, 33537, 53390662, 26681, 448, 378760, 1161551, 45, 16630221, 246687, 29488, 118245, 14, 1050, 3521791, 79566, 14459608, 59446039, 167, 148389940, 35, 199682, 3181585, 27, 234507290, 81, 77, 170284297, 1129, 10, 3156, 36887, 342868, 795512189, 977, 102363179, 6, 12692960, 0, 816962, 100613, 15843, 174632934, 1300, 1484618, 0, 4, 4070, 42, 909869, 1, 198204065, 32094, 4563, 4182227, 3079824, 54044, 47186, 3916, 10, 22, 27934921, 0, 183499, 124233, 25, 61243, 1019581, 122690, 69989423, 29, 2180, 72012, 1, 62, 34, 20809020, 0, 776, 25501, 4, 2013, 0, 245, 253941896, 19, 814671610, 1978, 1, 2234606, 4767, 2978143}

    310635569

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  23. {5395615, 63, 39758, 306, 33219199, 34, 12, 12, 1324, 111763888, 467242584, 168330917, 172706057, 996699721, 6697, 1425661, 458802, 0, 324596570, 5462, 1184912, 5, 4, 24090690, 0, 28, 4, 65869151, 4340700, 5}

    819275571

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  24. {10, 185, 8, 2698, 4335, 2, 1943330, 36916, 14330362, 109, 176, 1, 146174613, 17, 53167, 479, 3524224, 146861998, 1539, 716239, 43485, 33, 126571, 97, 8029, 0, 9264802, 225792467, 475522, 2, 441402, 48, 635, 341835, 498407, 235851673, 219143, 48, 415728195, 2008252, 125, 29, 2860, 1, 584617828, 98683880, 2, 189, 10482, 312475, 2131838, 218398, 276, 821216756, 1787, 1347, 315646701, 6350814, 3, 126732, 1763146, 465095, 25, 7, 6266, 94, 586375456, 17, 13505081, 964138, 24495, 191118539, 298715591, 3239927, 23912972, 35285, 792, 14, 4, 86, 2858481, 320500, 3374, 129, 829992605, 5677742, 33328, 846563, 107039439, 1907788, 229267, 762, 365, 1755054}

    982582409

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  25. {1457, 13, 34667, 10619, 111648, 240426597, 2, 3, 87793390, 735734637, 44852369, 9327, 55, 1851492, 63, 2392777, 1044930, 35, 0, 711, 2099, 14, 931721535, 77, 89, 3103, 251910, 30073319, 8058, 1, 11, 1742, 86908718, 2294964, 71991808, 10, 17, 0, 3595755, 381647124, 140461997, 41502, 0, 7075694, 6316075, 468, 86327405, 15461, 21, 60712, 0, 10, 20535, 246169307, 1075, 0, 251344, 51, 44817377, 206, 1919689, 26, 161374251, 227580, 194020767, 5961422, 502010, 11258, 99, 0, 39979293, 2244, 1149, 8830, 6, 728, 1044, 1478, 44, 26, 113, 75153188, 1291813, 14, 884, 16154, 16318, 175423, 143976901, 7902}

    497913056

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  26. {23, 29861, 9167513, 1647, 391193, 32524595, 90, 3, 941837660, 187989, 17157, 766, 53, 6073817, 0, 2214, 54678, 108416, 907925257, 1006115, 17950514, 179477, 9974164, 36, 402884979, 200835, 2162, 20067196, 56595, 7695991, 218, 412084224, 2710222, 20557, 341999, 434576185, 279, 490256, 1818, 3942826, 268883567, 200, 24722, 14847060, 22, 480779080, 7935, 1, 19543, 52460, 3632284, 50050685, 78538666, 149432, 1, 208}

    195849254

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  27. {422218912, 53, 5, 32978157, 11470616, 3, 1, 75518248, 1096, 252535887, 2, 23323, 18, 18, 92769982, 43, 187508, 240304134, 8132451, 2204, 22470430, 35, 1762573, 3, 63057, 31673882, 121682695, 126}

    133

    Returns: {1, 2, 3, 3, 5, 18, 18, 35, 43, 53, 126, 1096, 2204, 18437, 21943, 22403, 22648, 23323, 23438, 25770, 27540, 29334, 29707, 30827, 30931, 31528, 31767, 32205 }

  28. {43944, 1861373, 344, 5538543, 271, 1, 37, 981871, 48340544, 66144, 175302907, 123, 4822, 36195, 22410246, 1851441, 431, 460, 19289, 401, 508, 324795, 55020105, 27805774, 968, 34, 264412, 0, 8332374, 63182, 1654692, 6833, 660694, 610540823, 1262226, 1458, 252, 423118239, 454823, 6841462, 44, 43, 89017184, 62, 1646, 28, 1719268, 231474, 4, 4153, 0, 56, 31, 4, 66, 36, 62148706, 5724, 81, 31108, 9687888, 25, 3, 1890823, 347, 11, 1783, 147, 686673453, 76247, 103, 1962, 5571078, 987458, 490900, 5, 2264401, 15, 27166319, 30451947}

    644179396

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  29. {1917079, 47848, 50430, 29, 320827, 6, 2821, 776854019, 2218, 9, 45639528, 933261647, 114494588, 975717, 286, 15312, 70199149, 143986272, 0, 2311071, 323977, 1, 80202, 199639096, 0, 84333, 501, 0, 3, 523161874, 22, 53, 78467379, 133964352, 4, 15480, 0, 1, 11583, 5177409, 236245, 946, 1349, 106540869, 8053, 196098, 488, 906, 53233, 62675795, 434847, 8242, 11}

    338484417

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  30. {297, 16500595, 613, 515, 2868, 12968316, 97896, 8, 1, 15, 26833818, 7, 5691, 7707483, 6, 934911}

    956080696

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  31. {201, 1, 68, 212413326, 536, 28971, 3257601, 965254, 354515, 1281198, 132557, 3577, 4949402, 91862, 246497, 42904, 109, 32829872, 942424, 1888, 846312290, 2737, 22, 28086}

    551597665

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  32. {1802, 170, 2269, 285424, 951953781, 123309, 549, 226, 2974, 2972, 1074, 6, 4, 3829504, 940320, 222, 3538, 1, 31121003, 21, 4320, 194, 1144, 4134711, 76, 108976641, 1198892, 8081, 115335, 1420, 1007658, 56, 27572, 200695608, 3192, 117528, 2454, 1028, 2128564, 99, 1, 13643, 12109, 4158, 838759344, 14586, 672, 926491110, 893, 57129348, 106, 203620682, 4358, 23201805, 286, 352391, 2379, 249, 4, 1, 343, 29013, 38307, 127, 6835480, 5926, 101, 316, 15, 1195954, 57, 30254, 1491595, 203612919, 139, 3597, 343, 0, 6660, 2, 12637391, 5501, 10, 11299, 56, 6302, 6, 493, 18388, 0, 47174155, 0, 4247, 7, 11239613, 12938, 13405, 7847}

    915292291

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  33. {519008, 193250104, 143, 8423797, 235978, 1, 1250625, 10691563, 281214, 252674, 801024247, 990, 1940, 1164, 1920713}

    681337029

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  34. {6, 0, 26746, 126879, 5, 9319, 802443378, 49, 31, 3954011, 61, 791, 354774, 509132427, 1490, 1, 349, 22459, 25909, 42860, 992843, 466074542, 22895, 4960448, 3110998, 4961, 3112303, 520, 1, 4, 146958667, 13709, 65405, 7287084, 9}

    70

    Returns: {0, 1, 1, 4, 5, 6, 9, 31, 49, 61, 349, 520, 791, 1490, 4961, 9319, 13709, 22459, 22895, 25909, 26746, 42860, 65405, 124299, 126879, 143514, 155014, 177387, 194437, 194518, 195909, 227575, 227721, 247125, 248210 }

  35. {2, 808278536, 676894132, 11, 6, 917, 7406}

    317017055

    Returns: {0, 0, 0, 0, 0, 0, 0 }

  36. {3740, 163, 5530, 2069723, 86, 8592, 21420273, 2185601, 1, 184844764, 693, 1841, 726, 7, 1348, 3, 2466, 46723614, 649178135, 6777499, 101298, 87081, 443102, 836445, 224, 0, 131, 419327, 5294, 151, 945, 16106}

    236316879

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  37. {1230, 5, 7056050, 456, 600888, 83215481, 278246, 511540, 64097, 1339, 28, 217185, 28, 23643861, 64, 11549, 77203, 27656845, 2, 2, 39385, 28783, 10589824, 443063, 3376967, 0, 54241, 8015, 8, 322173, 390, 74752, 1, 301597, 4, 157539, 869690675, 7, 32835189, 215082, 61, 756, 27, 1, 16, 3, 517744771, 125, 215608295, 61330, 87484676, 419, 15612509, 794902, 19050298, 1387, 14476350, 1, 749717, 1, 0, 103, 202530, 1267864, 1092490, 94314280, 62704, 12342381, 113, 7024, 1596, 12354, 385, 177711, 837910, 785934535, 71484, 3251146, 699669800, 13784786, 18143585, 9554, 0, 304067426, 847452479, 90, 78}

    690

    Returns: {0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 4, 5, 7, 8, 16, 27, 28, 28, 61, 64, 78, 90, 103, 113, 125, 180, 180, 183, 187, 188, 189, 192, 193, 194, 195, 197, 198, 199, 202, 204, 205, 206, 207, 209, 210, 210, 211, 211, 212, 215, 216, 219, 220, 224, 228, 238, 239, 244, 246, 249, 250, 250, 250, 266, 271, 276, 279, 289, 290, 292, 293, 294, 298, 301, 307, 307, 307, 309, 314, 317, 323, 333, 333, 334, 346, 347, 359 }

  38. {50752, 89096288, 205976708, 4799, 3769, 6662099, 4, 0, 43, 132650416, 1747, 955, 0, 143, 450634378, 279495, 145109703, 7, 511, 7334, 29771631, 200, 43929334}

    344836528

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  39. {7503613, 3615842, 515859128, 15580, 32278829, 716, 530, 874621881, 1, 39645380, 7, 127342, 24742, 3888, 1174, 909608, 3156, 639575670, 123996, 15, 13, 1, 32501, 20, 17552, 114, 411155, 139, 9038, 836887624, 40444519}

    345

    Returns: {1, 1, 7, 12, 13, 13, 13, 13, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 17, 17, 17, 18, 18, 19, 19, 20, 22, 24, 24, 24 }

  40. {560968150, 979, 514081411, 60, 1, 4267, 186, 833, 31, 247570321, 209399, 868, 292393076, 32577, 293, 126881978, 22, 142, 55534, 1647, 19, 52, 10692070, 236262, 28, 31106214, 129195, 103, 5, 626, 12504, 12, 153, 6722, 18, 80, 176914584, 6120683, 1, 569, 42241620, 3, 0, 580667, 1037, 6435935, 257, 180785078, 11624, 794503634, 905, 434479145, 10428337, 10131712, 311249273, 127570046, 0, 90738619, 351, 3, 3, 12236, 24921, 13769395, 277, 0, 3368, 46306850, 174746, 19, 8078, 89783056, 4, 642813341, 123168, 1068, 51174, 178954, 16872}

    173183773

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  41. {399663148, 156, 1722, 1653492, 1011594, 39822, 24367, 1, 516592, 4776, 0, 29, 212043954, 4672414, 192, 1, 4, 50688, 11061, 89456, 30, 2, 56161, 950712651, 1, 939566905, 504, 1718618, 608171, 221, 18, 437309039, 175, 126701471, 142342285, 7410, 8103, 119383, 23341, 61324, 4477893, 969626, 747272, 0, 3892, 26708634, 218, 18, 306, 53061652, 30888357, 601993422, 20379, 493273326, 1, 2757066, 39, 28, 6, 0, 49474331, 62, 31, 735697362, 812704859, 1, 21, 22, 31, 10817093, 7672268, 46, 82421, 47451, 13015560, 10, 55, 8898, 6, 283, 3, 1451, 11561}

    1038

    Returns: {0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 }

  42. {49701, 40719, 434525, 50, 294, 2219184, 900, 4395579, 14, 363429496, 3, 1241, 3254893, 108, 4353285, 344300, 55587954, 60483, 174152, 0, 34}

    246086101

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  43. {619010, 265842, 18474674, 7, 317, 5985, 36145948, 61918899, 7, 13, 30, 5764, 28, 46740, 7603, 112, 700307902, 4658770, 257040018, 50, 1615679, 14, 3, 5, 206984, 456395, 53, 90, 1, 168469, 201, 67, 217969, 25024, 69166009, 14504576, 24469, 3257924, 10279276, 43934, 7, 1, 217259, 35525, 902, 19105, 15728364, 146, 698, 960165, 4, 10571, 3497, 971929, 0, 30437, 22884837, 58, 1494, 1, 3}

    270

    Returns: {0, 1, 1, 1, 3, 3, 4, 5, 7, 7, 7, 13, 14, 28, 30, 50, 53, 58, 67, 90, 112, 146, 201, 317, 698, 902, 1494, 1748, 1770, 1782, 1875, 1889, 1898, 1900, 1902, 1919, 1961, 2076, 2110, 2206, 2220, 2255, 2274, 2388, 2418, 2509, 2632, 2642, 2671, 2745, 2793, 2882, 2921, 2992, 3058, 3128, 3155, 3181, 3234, 3394, 3405 }

  44. {29175106, 793, 195, 29777523, 321980336, 23311, 517601234, 188, 14519408, 11540, 1, 3, 119070789, 191010400, 286769, 421206, 5, 0, 5871, 90, 382769324, 1223882, 2, 2, 1617, 480, 86339, 115738, 14092, 3951654, 0, 1568, 2370007, 1014, 195, 29720, 1653729, 144736, 13883, 2103, 8103, 3, 451864469, 45026, 1444577, 456, 5036703, 164004395, 42338376, 1709}

    829508952

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  45. {32, 1, 314241, 2006157, 134203, 2, 9537021, 11589, 49, 123, 406881637, 44, 48430473, 2852, 317093, 403891142, 7302, 22, 15, 160452667, 249, 36549, 41125064, 40407}

    288

    Returns: {1, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7 }

  46. {2264, 25, 145584, 439706, 2764, 27, 3, 16426, 7, 1, 15461480, 49, 7607707, 9316, 1, 996262608, 0, 13991401, 11, 3, 465794, 15123, 751, 16676427, 375, 3, 52162530, 1078981, 435611706, 3528, 358732165, 7, 62859, 99783, 1625, 786235, 53193, 114, 928, 120276505, 195173, 35, 48, 377, 1333082, 234768475, 442, 130520368, 183964764, 2, 405, 10377764, 48637, 201985913, 163100414, 301422, 511, 2883, 11, 9, 0, 106, 83, 1249, 14, 1763359, 250, 15731581, 484460, 15709, 49915, 175114, 6069781, 14, 679031030, 12, 2, 41779951, 76195, 1, 13540, 237125099, 15, 0, 131554577, 1838, 33118, 57812, 7450, 1, 289, 2329, 1863603, 72, 0, 50}

    743923071

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  47. {38, 10657873, 13161, 3126301, 2498, 136423, 53, 32, 1317, 498, 2296673, 378161, 373084, 245208, 22591326, 759323862, 991, 0, 44785, 472088, 340875629, 488, 24907628, 44472768, 117, 16516729, 82322, 28, 11, 380, 13751931, 5792361, 228, 200787480, 6267146, 14708, 9, 14, 3961, 2562, 11315, 57677, 1896871, 13922436, 10904, 11, 11, 576543377, 2442, 63, 113463, 304896, 5562, 7, 5714867, 109976, 3341, 3603, 15, 41749847, 97658417, 11260872, 16255420, 57017688, 3, 852, 12355, 72, 18, 0, 1, 11124851}

    641096072

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  48. {228901, 439053, 659, 866, 17650099, 29447774, 1709, 1718, 642, 162, 59836, 793, 0, 676, 4, 25, 582}

    106

    Returns: {0, 4, 25, 40, 41, 42, 49, 53, 53, 53, 54, 55, 56, 58, 67, 72, 80 }

  49. {36893, 27511838, 10056345, 31, 17751544, 63227223, 99998716, 6269, 15315667, 0, 74733, 44425, 96, 9, 829468, 13, 6073579, 2926, 83, 10464, 137, 22446, 8131968, 4184947, 13037347, 71422, 1696, 5451, 1387, 121343745, 1544442, 243, 60203948, 10, 355580993, 29893, 108029778, 11094463, 30, 112556692, 73, 3281241, 0, 757, 16, 3771, 66, 41, 69, 1, 74766, 891646242, 5934, 163011, 288627844, 689645842, 38386934, 161, 26389905, 3792, 937, 171234, 921209782, 17299834, 3629156, 1095850, 113714086, 211, 32125855, 53, 170725360, 5264, 1946472}

    708441890

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  50. {1623843, 1, 0, 57116, 1, 1473752, 7, 22375, 28940162, 55, 6361274, 18, 17518997, 234, 9288, 1, 0, 0, 52953, 67477834, 8868781, 6, 218542249, 29042917, 657288, 792128, 18493834, 5973794, 4590, 404756, 268, 24, 10, 942140, 46345938, 13592, 1, 146764, 1531811, 432494464, 4506523, 768397236, 27052, 1776, 17, 23, 42720, 7, 329973, 6397, 451, 76417, 202, 935119846, 5, 2429, 716123822, 25, 419842, 52, 113050, 894854285, 201488, 966252049}

    815427203

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  51. {438441, 5949, 0, 916, 26278214, 12314522, 911751, 915244549, 0, 6701, 13514, 18328040, 717, 150, 82407063, 5, 113, 77, 186464, 44261894, 68654, 1, 189554686, 0, 3036401, 48155, 289, 92670946, 29552, 749037, 30159850, 0, 11725575, 387778545, 7, 26503, 74, 231435, 2740, 24, 1420, 3982, 1, 1960868, 3, 33017984, 2249617, 512792, 508839337, 3, 43508190, 30664167}

    535

    Returns: {0, 0, 0, 0, 1, 1, 3, 3, 5, 7, 24, 28, 28, 28, 28, 28, 29, 29, 30, 31, 31, 31, 33, 34, 34, 36, 37, 37, 38, 39, 41, 42, 42, 44, 44, 44, 44, 45, 45, 45, 46, 46, 46, 46, 47, 50, 51, 52, 52, 53, 54, 55 }

  52. {415, 8802941, 165, 99647, 43919250, 0, 2683441, 295325, 190541, 7019217, 5495821, 850176, 279015, 15699, 25300571, 412, 1, 240, 49054, 2029338, 291821677, 37058485, 33640, 115, 1433, 140, 221245054, 56108, 123414323, 24106384, 374, 649626, 96, 556089, 1, 69, 15, 3255806, 8, 12593462, 21748, 1, 686430, 237, 91917, 364042230, 171591, 17624183, 19, 545, 7558342, 880888, 73, 79611387, 24059118, 210492, 988714, 1972, 907813, 1}

    398

    Returns: {0, 1, 1, 1, 1, 8, 15, 19, 69, 73, 96, 115, 140, 165, 237, 240, 374, 412, 415, 545, 1074, 1075, 1086, 1089, 1113, 1130, 1153, 1214, 1268, 1310, 1340, 1340, 1340, 1341, 1359, 1388, 1433, 1436, 1468, 1471, 1488, 1532, 1537, 1544, 1556, 1589, 1644, 1660, 1687, 1713, 1720, 1753, 1773, 1845, 1883, 1931, 1962, 1972, 1981, 2102 }

  53. {293, 22318, 0, 29078, 407762096, 136749798, 453, 7753265, 632, 10030583, 108945, 19353, 43, 2, 3, 18, 94, 126382056, 8311904, 982663, 1, 501, 780891065, 147, 293975727, 12, 99587, 6909445, 227675902, 11619, 14663}

    262283869

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  54. {74003, 82446737, 90, 5320, 12594364, 383948447, 47863, 1938521, 95976910, 162, 470, 41695, 13487562, 2233, 74812, 4006927, 33576, 14, 0, 1467, 3108041, 283, 63582926, 5647, 4692930, 366589242, 945, 3717, 8129, 10659, 40610, 42196, 106033, 4425, 2, 7771, 3, 40, 494, 6642, 861, 1, 22875908, 0, 13, 221, 51, 2, 25953, 14, 933242475, 195588753, 40016, 30, 63, 18, 0, 92033, 2, 8216682, 3234840, 133968, 33, 797069, 3, 58867, 6756, 6660104, 3146, 307868, 4, 131973651, 325733804, 14413285, 1914, 12, 258834, 16017, 24300, 501, 2778, 1730093, 11238, 1346, 172511, 130751636, 64505, 565, 6080, 60479, 1, 1472}

    665608381

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  55. {36, 207138, 1436, 103622, 81183609, 5177092, 3921037, 48297991, 532, 7393, 118, 0, 7532094, 1, 3112696, 2, 1811870, 29214529, 179902, 29822001, 1639, 1260, 29675805, 8638403, 861772, 147, 3376095, 142056731, 2, 1, 0, 7907, 462, 15200522, 5, 20, 4, 46, 1381, 0, 32191969, 3443, 96473622, 17477613, 190169446, 3348, 166759478, 652796, 1, 48, 118827839, 1, 5900402, 11994, 535737998, 12437, 1947880, 12938452, 23229589, 8, 453, 503, 23297, 214689001, 40214931, 953119, 1547, 194264, 3435, 2020046, 24, 33857, 7, 308670, 1, 7988592, 113420915, 351, 272183, 11421}

    523001412

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  56. {74955322, 17658918, 1, 177299, 2, 2, 277, 15464078, 826632, 128, 39, 2569, 128023, 18, 0, 6575, 139268, 1, 10095, 34, 68, 5277, 422485812, 2329614, 322836, 23660539, 0, 58777, 144, 514916088, 3716949, 486579646, 6197857, 360322032, 272492, 2653763, 3564, 3631, 53286932, 167223, 1007093, 42859, 109626459, 1756488, 134764627, 3298, 18, 14150428, 485787835, 12546, 807226, 17, 4506, 5, 2905933, 816, 4130100, 715220, 86, 307, 582396, 2998, 9335649, 396055487, 846390167, 4488604, 467483, 28, 7, 1371, 17, 8, 451666739, 28108, 9757, 841869, 900583, 11, 0, 5418, 82282911, 2314, 44, 1887, 1809, 3, 701, 7768048, 470604046, 33, 6, 124305542, 17, 586, 59211556}

    702

    Returns: {0, 0, 0, 1, 1, 2, 2, 3, 5, 6, 7, 8, 11, 17, 17, 17, 18, 18, 28, 33, 34, 39, 44, 68, 86, 128, 144, 277, 307, 334, 338, 342, 343, 346, 349, 350, 354, 361, 374, 377, 378, 392, 394, 402, 403, 403, 406, 408, 410, 411, 412, 418, 428, 430, 431, 439, 439, 445, 448, 451, 452, 453, 453, 456, 459, 463, 464, 471, 471, 474, 474, 491, 491, 500, 504, 514, 532, 538, 544, 547, 563, 568, 568, 569, 571, 578, 586, 609, 627, 630, 630, 642, 647, 653, 659 }

  57. {1018, 510085, 148, 729, 1039, 2, 254519623, 47686, 1321, 112, 8107946, 1822892, 13563729, 2554, 523838716, 759945, 615657497, 703, 175, 1873, 2, 3326093, 816516802, 538882039, 759378, 19658, 534829852, 98, 732834, 38824366, 39840508, 0, 111, 875, 567696718, 15450804, 77331, 56313525}

    747779906

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  58. {140, 746909562, 9263636, 1, 3716, 5373, 781947045, 203990874, 1, 258, 132113093, 7254527, 829411640, 2831, 280162, 416051, 7345, 40717374, 136063115, 110, 0, 49, 1581, 143, 9, 10082705, 64719071, 8258620, 23017, 59, 344313, 14067503, 1404, 179501, 1291818, 20, 183836, 2, 52, 0, 20482, 271087, 271192059, 30487, 3946, 3, 13, 60859679, 89717, 2801984, 162, 166183429, 6564, 2, 122684, 6, 255, 5447, 35, 1960}

    645031515

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  59. {59, 1699466, 0}

    794806083

    Returns: {0, 0, 0 }

  60. {87081, 93953902, 13, 62901413, 4050212, 306256000, 15127728, 7, 172057988, 0, 2, 192715, 46407085, 32, 587, 1791, 3695, 8, 126616354, 326601, 216, 15099, 3, 23239798, 1063099, 409546019, 6, 7, 67587, 405, 1252825, 613979263, 1, 4942, 63, 31750897, 641240, 11618, 3894943, 139124952, 288023, 301992, 26, 13, 1449, 744, 3706966, 109521514, 122283444, 9448979, 34311, 15991862, 10017820, 55697026, 1, 343852, 8380129, 119015789, 1122, 3396269, 997, 470103342, 442469, 117, 0, 14019076, 109, 16959}

    832318899

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  61. {29, 444961672, 2030071, 585061087, 41214, 1002, 6}

    106

    Returns: {1, 1, 1, 1, 1, 1, 2 }

  62. {535604, 141156, 1186, 509630769, 7794, 353591828, 459, 14, 5, 2949605, 652571335, 238531348, 1175774, 159, 67442, 1859003, 2, 12, 503334, 10718645, 12134281, 78918454, 3643, 13287081, 51, 21, 149346, 11095, 278653437}

    390163270

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  63. {59081806, 0, 0, 53, 129, 2054, 14519209, 204209, 899160052, 197602, 1, 2, 63, 126803437, 40562728, 65048246, 63791864, 104124668}

    515097439

    Returns: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

  64. {68, 37, 3071061, 5497806, 125967, 34345, 70162, 951494, 65, 464215, 9673, 3580, 11, 9703858, 12916841, 64, 716811824, 12, 10789, 859, 1194707, 18528, 771746, 4432844, 263113, 17834, 0, 27617, 333, 71422970, 833524729, 123, 46558880, 314, 63082928, 5480841}

    454

    Returns: {0, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11 }

  65. {12274, 1448296, 445982, 14, 2, 967957831, 2794, 42390479, 173140662, 449662200, 6744, 0, 47549442, 757, 29762806, 51}

    129

    Returns: {0, 2, 14, 51, 725, 757, 767, 843, 857, 871, 908, 923, 1293, 1320, 1397, 1414 }

  66. {1012402, 77112, 55696989, 226520285, 24966, 21241801, 2, 358496, 1601321, 36477996, 389717825, 888, 13, 251902, 245377, 607643595, 55201, 3890043, 7, 1491115, 537956551, 5732, 152234, 1449328, 300792, 7581656, 765, 37, 538674437, 35630372, 48, 327, 1555002, 3762, 42, 63530, 7, 31, 1295670, 40998137, 13145, 1, 563835, 0, 20002, 9, 2, 3326014, 17243599, 7123011, 953443698, 7476, 1664, 72744, 49698, 25293, 32715, 326, 15564686, 2865, 72077, 2, 26526466, 6523605, 1, 121026, 8312352, 462288425, 757340078, 43, 101806, 72, 77257, 5548242, 197972510, 1778}

    988

    Returns: {0, 1, 1, 2, 2, 2, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13 }

  67. {11, 13 }

    1

    Returns: {6, 11 }

  68. {21 }

    1

    Returns: {10 }

  69. {0 }

    1

    Returns: {0 }

  70. {123, 4568, 89123, 45, 678901234, 1234567, 12345, 12345, 12345, 12345, 12345, 12345, 55555, 55555 }

    20

    Returns: {45, 123, 4568, 12345, 12345, 12345, 12345, 12345, 12345, 38580, 41436, 44561, 55555, 55555 }

  71. {11, 13 }

    1000000000

    Returns: {0, 0 }

  72. {8, 8, 8 }

    11

    Returns: {0, 0, 1 }

  73. {123, 4568, 89123, 45, 678901234, 0 }

    1000000000

    Returns: {0, 0, 0, 0, 0, 0 }

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