Statistics

Problem Statement for "HalvingEasy"

Problem Statement

Halving is an operation that takes a nonnegative integer X and transforms it into another nonnegative integer: the value X/2, rounded down if necessary. For example, halving 16 produces 8, and halving 21 gives the result 10.

You are given a int[] S containing a collection of nonnegative integers. You are also given a target: the int T.

Count the number of elements of S which can be transformed into T by halving them zero or more times. Return this count.

Definition

Class:
HalvingEasy
Method:
count
Parameters:
int[], int
Returns:
int
Method signature:
int count(int[] S, int T)
(be sure your method is public)

Constraints

  • S will contain between 1 and 50 elements, inclusive.
  • Each element of S will be between 1 and 109, inclusive.
  • T will be between 1 and 109, inclusive.

Examples

  1. {6, 14, 11, 3, 1}

    3

    Returns: 3

    6 can be transformed into 3 by halving it once. 14 can be transformed into 3 by halving it twice (14 halved is 7, and 7 halved is 3). 3 can be transformed into 3 by halving it zero times. the other two elements of S (11 and 1) cannot be transformed into 3.

  2. {42, 10, 10, 10, 11, 11, 20, 21, 39, 40, 42, 43, 44}

    10

    Returns: 9

    42, 10, 10, 10, 20, 21, 40, 42 and 43 can be transformed into 10. Note that all occurrences of 10 and 42 are counted towards the answer.

  3. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

    1

    Returns: 20

    Every positive integer can be transformed into 1 by halving zero or more times.

  4. {987654321, 1000000000, 998244353, 123456789, 999999999}

    476

    Returns: 3

  5. {987654321, 1000000000, 998244353, 123456789, 999999999}

    1000000000

    Returns: 1

  6. {705084822}

    1

    Returns: 1

  7. {705975753}

    42

    Returns: 1

  8. {861648772}

    42

    Returns: 0

  9. {476190629, 766098599, 192550219, 560689959, 450968417, 982631932, 880895728, 707723857, 910286918, 404539679, 317063340, 287341521, 8225926, 827727492, 492601449, 191890310, 782177068, 818008580, 877021269, 441583657, 866723754, 753778917, 289848404, 360026868, 475402312, 363001098, 883370112, 615347366, 366915360, 909179156, 933195036, 506147731, 816248153, 37119022, 215208399, 189766466, 137831502, 47628333, 409233792, 888987010, 87027328, 216092612, 34634935, 44991256, 711107839, 278886803, 590039012, 473809695, 214794839, 133275785}

    1

    Returns: 50

  10. {956435856, 654180081, 792345559, 632488502, 70422962, 26697435, 399367956, 67799919, 496961705, 392416704, 879381297, 186880274, 782471604, 938207958, 313902510, 580229736, 581733169, 43715109, 582439611, 184781011, 93498228, 17902428, 263034618, 275716851, 751692737, 590874751, 553563329, 984208672, 423181584, 310197015, 214278326, 936333553, 989214957, 98938314, 637212549, 144550948, 394002980, 675711460, 747706472, 243110421, 86624645, 354745177, 599445810, 800910535, 637742892, 101430412, 801006699, 99958976, 458482217, 770179343}

    2

    Returns: 36

  11. {956184425, 253355300, 915528475, 415240538, 991524100, 900438653, 210218996, 523385535, 524960268, 834335761, 106009564, 782327307, 661126878, 974961152, 515755560, 249840845, 73219320, 209547798, 528665049, 55881990, 217537575, 97276752, 133445606, 806813442, 945634152, 898789462, 429355922, 16497484, 646193559, 486806201, 400861649, 912104186, 402027370, 216740273, 250153750, 112395983, 901084367, 841379368, 261898711, 416895433, 107168806, 236160557, 515439799, 850640289, 889704917, 275127176, 534407965, 816353541, 467510003, 976959064}

    3

    Returns: 42

  12. {51853974, 145402024, 129816176, 350891151, 469899876, 68350397, 79806463, 272041611, 42073915, 561747480, 166275394, 290237604, 861769143, 700175183, 611476420, 640815479, 656643014, 12729744, 621339268, 175893929, 228623399, 601503952, 581236420, 240008060, 923749745, 184258241, 55762240, 35043830, 748071459, 948580482, 157390034, 883015569, 29948938, 254961810, 71758606, 472296375, 945945121, 619782776, 571628782, 138292912, 476717409, 618719779, 406765063, 677847358, 568907333, 417219069, 578686766, 797833208, 591982401, 911573750}

    4

    Returns: 23

  13. {675637612, 784627756, 187327593, 17493698, 337042889, 941158190, 357153925, 765567162, 731493713, 178506814, 61164523, 137966448, 714007947, 419053521, 399523325, 786473207, 3142445, 98692691, 100257624, 644322683, 476275226, 832102486, 372173908, 174357259, 851363568, 980050276, 725043304, 775495557, 678259131, 461040436, 11670626, 395414811, 742270777, 674208918, 851016755, 648002202, 372008850, 22417472, 100139101, 345302333, 736632350, 196240539, 390672614, 67293221, 772274459, 747445439, 596033393, 521774105, 727188617, 38233807}

    5

    Returns: 33

  14. {130122780, 947875781, 995380548, 472850413, 972025954, 124226645, 476962253, 519466935, 183856471, 437681121, 989792135, 307481289, 526104418, 529627209, 484889823, 509214376, 60777099, 509344364, 787896434, 12159384, 967603974, 417904432, 79841635, 948994953, 437626345, 980764501, 487680137, 260882088, 971596103, 950708526, 997942367, 977836137, 535913054, 130408000, 519223966, 471938288, 784914566, 498950131, 636141112, 61626146, 258668370, 215990441, 998366119, 943178355, 974553602, 103175359, 262495177, 236311230, 15942251, 66486892}

    7

    Returns: 38

  15. {704749873, 691317942, 679098226, 659420933, 491851583, 735210724, 599463599, 217756825, 961112922, 179086841, 219085843, 986106314, 999698901, 189188535, 546078275, 84393837, 736921167, 409426952, 622379916, 560284916, 337724607, 685965301, 431045101, 888635433, 568711277, 884238645, 913613324, 20653889, 87425243, 360117961, 366783581, 776314619, 468286477, 571284025, 168626134, 583233179, 647468697, 159251051, 858990763, 810722471, 924525652, 326078850, 833618000, 822365411, 370156626, 483777764, 472155517, 42439764, 683053801, 173959990}

    10

    Returns: 16

  16. {196280475, 455534340, 377106690, 110361918, 670255789, 128987489, 554966626, 872829891, 183199736, 423654107, 447285332, 493312766, 220238159, 771949652, 926551968, 376139905, 936004372, 949988937, 13919652, 308544142, 827810140, 623050074, 450752159, 963696419, 398374721, 740843615, 981685674, 778648246, 442566186, 891971332, 395985201, 802072604, 111650189, 479737129, 246622746, 525998319, 618533824, 712849045, 242901511, 366044199, 739274655, 936050497, 454606024, 894065096, 924332136, 918447387, 292855310, 230869323, 745446305, 678939399}

    13

    Returns: 18

  17. {386425020, 171177723, 701900415, 171753246, 685290494, 682557844, 85070784, 696402251, 394611413, 389151686, 52447487, 685438660, 686475545, 379651586, 124545298, 502670251, 701989574, 464293056, 5493474, 87284189, 873542149, 5318979, 170474885, 341292187, 86833268, 85316891, 696363690, 758648646, 682967525, 39940010, 236223640, 681889838, 676018702, 336399710, 170375737, 712383395, 346345029, 330942460, 171230032, 695498755, 346570174, 682802893, 704641895, 170035538, 683565808, 5407721, 674955168, 694086459, 42173562, 845035969}

    20

    Returns: 35

  18. {788543784, 199689851, 397143694, 96787256, 193466617, 199444412, 794827414, 802992013, 784173591, 790414085, 49398315, 288875070, 804610877, 99346960, 197667226, 621304410, 389704508, 792043758, 796362653, 801458127, 98536408, 393668806, 197865936, 796081862, 781785045, 396236020, 399848319, 141418696, 521447585, 400160148, 196590836, 7858139, 777215875, 99380278, 195145308, 373949193, 995018150, 390053857, 24204483, 398000295, 783051009, 776033621, 780582363, 386706272, 795135063, 389953977, 800896587, 779073201, 193097448, 940421369}

    23

    Returns: 42

  19. {811430570, 424823451, 310234370, 28742673, 177792920, 978362371, 553244458, 719754412, 179727272, 356053025, 80927971, 870383607, 89710344, 717746712, 483322438, 139502203, 965597251, 708934475, 722388045, 344216654, 356374977, 155885707, 230276742, 596097382, 89417416, 719901615, 548335008, 266026606, 758032489, 207704143, 463216698, 173638436, 180136302, 369101338, 353865469, 716842415, 724872778, 88916678, 216478952, 250930049, 713992012, 360034515, 479567318, 8867391, 446677823, 44411150, 654239301, 704697264, 25330661, 140740989}

    42

    Returns: 18

  20. {325153034, 583306397, 648463600, 650551031, 652299468, 326682274, 859028226, 650272670, 80875190, 647254065, 653773564, 111917168, 859927425, 323898669, 16317200, 324366506, 653510827, 864295865, 600358504, 653761659, 20383991, 325855823, 444130863, 647139692, 324538327, 324775113, 301313047, 177893812, 867768593, 559078422, 647639004, 648580004, 81577110, 654228445, 649467983, 654227871, 647412191, 647770853, 162455804, 611678054, 291627415, 754762260, 682556895, 653868496, 10182169, 651477462, 693035862, 651373901, 326874096, 372334274}

    77

    Returns: 32

  21. {519382077, 20951359, 890883231, 644075805, 200834115, 129862481, 570081388, 158580531, 519961040, 517643627, 65811660, 968799590, 109102235, 441114664, 610338520, 304489019, 158100373, 259281246, 590662720, 517121722, 639052960, 610066926, 818442884, 257956338, 8082374, 9442349, 365177396, 197720766, 453569111, 790318645, 222486377, 697253713, 274400592, 348825537, 26996264, 916411562, 641283774, 406528293, 270883607, 968262334, 516270545, 519228881, 258105408, 517607220, 895405762, 32461769, 129846335, 667905574, 336104387, 879836673}

    123

    Returns: 14

  22. {918788727, 647133298, 647287596, 647417595, 323695465, 647318374, 40461728, 647218457, 161801361, 647298365, 647181908, 20226158, 647288120, 323737517, 562253743, 647002548, 913678360, 647153629, 647175500, 647183507, 647461310, 161799916, 323617585, 647149807, 647392661, 647214312, 647469051, 161769226, 647238563, 161786239, 647073088, 647460886, 647437058, 647325754, 647189460, 647102481, 647129619, 647053067, 323635897, 647021790, 161829467, 647071962, 323647488, 647456150, 132090107, 80883981, 647190249, 161841472, 80900881, 40437850}

    1234

    Returns: 46

  23. {951883261, 351978837, 202263186, 685750717, 784669494, 809089358, 344968742, 169764728, 396719589, 809057586, 809062788, 404536043, 128935318, 202275178, 323792535, 610450725, 311666807, 404549231, 40533657, 683573491, 408099670, 311619089, 259302023, 599303182, 499317530, 501559962, 654715809, 380620105, 809093344, 308635082, 809053870, 404535167, 809061725, 809059426, 311597689, 809074556, 101135580, 101488655, 466683986, 174051828, 313739731, 658011496, 14653719, 840033224, 417016757, 809054986, 763440169, 941105516, 199917587, 809104887}

    12345

    Returns: 16

  24. {505679218, 126419479, 505676779, 769840622, 252837888, 796312013, 80190138, 221479259, 505675927, 505679413, 272364918, 913495663, 12675627, 562517113, 505676457, 126419614, 878985664, 165123224, 986457010, 383113089, 375071921, 213283892, 252839582, 252839171, 126419851, 372984101, 779135380, 505677926, 382268543, 126419826, 126419309, 126419498, 357270837, 683664096, 647150823, 742438973, 945531896, 505676226, 353542015, 505678236, 505678184, 31604756, 505676968, 317154902, 252839436, 421657505, 126419415, 63209866, 591343614, 380904091}

    123456

    Returns: 23

  25. {632098558, 632098741, 316049244, 19753081, 9876543, 250292194, 316049234, 316049374, 632098717, 632098558, 632098531, 632098746, 632098616, 316049297, 316049276, 632098392, 4938270, 316049370, 314922396, 971016913, 39506158, 632098711, 79012310, 632098486, 316049226, 316049215, 751440732, 632098508, 159900545, 39506147, 316049391, 632098799, 632098633, 389708391, 632098602, 632098718, 316049308, 316049326, 158024642, 632098538, 632098700, 316049322, 632098420, 316049260, 923696609, 632098635, 632098313, 632098642, 19753087, 632098656}

    1234567

    Returns: 43

  26. {726664558, 395061727, 197530862, 790123423, 328410628, 99012174, 49382715, 790123398, 181662118, 395061708, 790123410, 790123411, 790123411, 395061718, 273814231, 790123409, 83758997, 702743810, 988541851, 737294799, 197530850, 98765424, 790123405, 790123429, 719736140, 790123437, 416808051, 790123422, 170162478, 197530863, 661757885, 790123440, 790123412, 790123414, 197530854, 790123408, 790123428, 790123438, 395061726, 815749174, 790123435, 790123417, 790123441, 610550631, 545437898, 363753823, 973862281, 371433403, 790123396, 790123415}

    12345678

    Returns: 31

  27. {484874603, 399704255, 788100581, 293768673, 416968230, 758997339, 709779554, 564974997, 846269522, 819969721, 88187828, 798904119, 235262152, 608780353, 384591572, 352373328, 680358050, 938602397, 987654313, 200182436, 24694360, 386958442, 393394491, 449212721, 977452494, 281662462, 772672943, 736941734, 678016656, 981818967, 507771063, 232106000, 513990525, 588097828, 493827159, 987654316, 156448639, 413488920, 987654316, 148986247, 987654314, 168781191, 54722828, 987654317, 465198262, 614654003, 987654314, 493827159, 974498854, 791026827}

    123456789

    Returns: 8

  28. {1000000000, 1000000000, 1000000000, 40422589, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 578811207, 613202515, 1000000000, 1000000000, 419393931, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 323645889, 372413726, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 816969328, 1000000000, 1000000000, 1000000000, 1000000000, 147211847, 1000000000, 1000000000, 1000000000, 1000000000, 928413563, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 693600522}

    1000000000

    Returns: 40

  29. {1000000000, 589903429, 500000000, 500000000, 500000000, 530814763, 577143973, 500000000, 343561197, 1000000000, 500000000, 1000000000, 838533890, 500000000, 1000000000, 1000000000, 963680175, 612293976, 1000000000, 56204850, 500000000, 500000000, 500000000, 500000000, 500000000, 150913508, 500000000, 793010334, 73542826, 1000000000, 1000000000, 366799595, 1000000000, 833087002, 500000000, 139381935, 561485053, 1000000000, 500000000, 593738221, 592204386, 501039932, 699156498, 1000000000, 115608096, 956123828, 1000000000, 1000000000, 500000000, 1000000000}

    500000000

    Returns: 29

  30. {323854598, 483645491, 63098328, 757708023, 188796716, 383876386, 169940553, 999999998, 999999998, 95417403, 191081960, 912001777, 430362076, 227812093, 900559367, 773599974, 600827340, 55760010, 8119584, 387901847, 499999999, 779549618, 721077196, 401325895, 992169478, 499999999, 747442053, 999999998, 677991108, 898979340, 429375646, 976992761, 944121352, 499999999, 570922747, 620352453, 454981733, 604327472, 64847656, 672121743, 720694973, 304581939, 284436975, 360556289, 520558429, 161631731, 456662012, 361827479, 573012372, 999999998}

    499999999

    Returns: 7

  31. {500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 355894785, 500000001, 500000001, 500000001, 38088018, 500000001, 500000001, 500000001, 124942227, 500000001, 500000001, 623515919, 500000001, 500000001, 557744980, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 61982860, 500000001, 500000001, 500000001, 143854382, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 500000001, 469506240, 500000001}

    500000001

    Returns: 42

  32. {405682436, 717856234, 588521503, 407114386, 22427550, 299530046, 283714567, 811364875, 405682437, 926033226, 567531866, 405682436, 651267232, 405682436, 663692793, 107598918, 375942025, 934187948, 811364875, 854153734, 621443036, 389722019, 811364873, 413996253, 811364875, 992860483, 84862968, 202841218, 811364872, 576772587, 461724003, 811364873, 811364874, 374640787, 811364874, 13130433, 979628368, 296977415, 608514039, 811364875, 949143837, 824808951, 811364875, 811364872, 988871720, 975849803, 748869734, 202841218, 236140080, 124228589}

    202841218

    Returns: 17

  33. {776864377, 399414281, 799730855, 366175305, 808881229, 99966356, 799730862, 799730853, 770441495, 902154120, 838360740, 833149304, 454995384, 624658678, 205443857, 482854891, 876367454, 917546095, 204503236, 200701267, 665075036, 401517720, 399865427, 487002593, 314640159, 799730856, 399865430, 220804895, 355002608, 949243418, 585564799, 999320448, 799730849, 454976636, 517289573, 904216626, 614629039, 60233007, 810739392, 799730851, 919782933, 799730856, 655063078, 632549570, 799730856, 415808484, 128905164, 449181378, 276929325, 110672082}

    49983178

    Returns: 11

  34. {847082175, 847082175, 812164321, 245253583, 847082175, 847082175, 227045241, 847082175, 549337451, 847082175, 847082175, 566267633, 319034496, 847082175, 441597604, 955413021, 765020460, 847082175, 847082175, 847082175, 527477943, 372302439, 346586881, 847082175, 847082175, 847082175, 847082175, 388239281, 412681936, 179105903, 847082175, 854457886, 847082175, 626463987, 847082175, 656468012, 847082175, 460865930, 847082175, 786550612, 847082175, 847082175, 847082175, 390487354, 783230321, 541196370, 847082175, 847082175, 847082175, 847082175}

    847082175

    Returns: 27

  35. {538439401, 906182030, 668767315, 476550283, 429307182, 226545507, 618678185, 464000525, 666010487, 906182031, 906182030, 906182030, 906182031, 453091014, 594558826, 783314105, 906182031, 966382003, 453091014, 152070905, 226545507, 506480382, 453091015, 646617327, 453091014, 97928445, 906182029, 491046228, 125742825, 386079376, 859153319, 453091014, 727109426, 778890548, 4800325, 453091015, 160444561, 114179443, 226545507, 453091014, 453091015, 584701309, 387443345, 523564831, 226545507, 895057944, 497644687, 568481640, 205705370, 984847250}

    226545507

    Returns: 19

  36. {672011292, 155483183, 365339698, 840238880, 411722254, 555432061, 730679397, 730679396, 533944704, 873731826, 229111169, 730679397, 128298713, 862875718, 523918054, 662605706, 365339698, 240671155, 639885170, 962411601, 365339698, 953565547, 730679397, 730679396, 365339698, 730679396, 218108340, 263565701, 399695188, 659967653, 595463229, 408566790, 527349557, 730679396, 162337220, 730679396, 730679396, 415843870, 188593660, 238583964, 455060723, 389083060, 730679397, 365339698, 344749927, 730679397, 365339698, 365339698, 848914734, 365339698}

    365339698

    Returns: 19

  37. {105621108, 904226743, 904226743, 452113371, 112148978, 904226742, 26656586, 41212056, 520462551, 452113371, 904226743, 778023919, 452113371, 984387339, 502749625, 165667173, 452113371, 904226742, 408183812, 599041143, 904226742, 904226743, 763947428, 645522543, 486079311, 836470904, 738782219, 904226742, 904226743, 904226742, 904226742, 904226743, 149088552, 452113371, 685868128, 233921633, 370336222, 652092655, 511961257, 395152544, 452113371, 841374134, 877463159, 452113371, 898651437, 795759764, 904226742, 904226743, 904226742, 245990926}

    452113371

    Returns: 22

  38. {875616714, 643093619, 643093619, 643093619, 643093619, 643093619, 643093619, 643093619, 975770527, 643093619, 597251880, 203937088, 569360127, 210616375, 643093619, 390919175, 462137649, 993121847, 748586543, 643093619, 643093619, 491622809, 643093619, 982248691, 288301845, 643093619, 643093619, 643093619, 347668392, 898818685, 643093619, 926915194, 643093619, 643093619, 643093619, 673137761, 574252341, 643093619, 643093619, 643093619, 962449015, 643093619, 643093619, 643093619, 643093619, 919061457, 81133080, 334452620, 855068019, 413994929}

    643093619

    Returns: 26

  39. {671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 671381373, 745457045, 671381373, 671381373}

    671381373

    Returns: 49

  40. {941119590, 941119590, 470559795, 229344783, 470559795, 470559795, 941119590, 941119591, 941119590, 941119591, 941119590, 707741658, 941119590, 640896378, 512649850, 47520647, 941119591, 941119591, 941119591, 813264178, 470559795, 941119591, 673255371, 941119591, 237441222, 567864975, 810229793, 941119591, 941119591, 941119590, 636873250, 217625970, 892241563, 470559795, 941119591, 941119591, 941119591, 211758353, 941119590, 941119590, 969113142, 941119590, 941119591, 941119590, 941119591, 941119591, 941119591, 941119591, 470559795, 941119591}

    470559795

    Returns: 35

  41. {228379612, 295260443, 854600116, 295260442, 206327713, 345922922, 256091438, 10839435, 590520885, 707304023, 790819730, 590520886, 590520884, 113632425, 834122252, 67128928, 590520886, 590520887, 443750046, 883671572, 637835615, 126500894, 295260443, 590520885, 591914800, 590520887, 91849258, 590520885, 950024750, 295260442, 180665018, 702696136, 590520884, 590520887, 590520885, 590520885, 266511483, 525274169, 302652314, 315198541, 508383887, 42326680, 147630221, 125347575, 147630221, 295260443, 590520887, 295260443, 154787389, 147630221}

    147630221

    Returns: 22

  42. {575535967, 976722762, 802816141, 931609794, 276870257, 438901961, 793120908, 774941771, 996729811, 611910887, 360331566, 328857966, 30397434, 290743913, 64836232, 401795217, 368095900, 390002005, 82879470, 105444695, 778848940, 280809199, 905627127, 768310951, 655137889, 206508989, 437276789, 153700004, 457473839, 496978819, 781666944, 829339828, 59016652, 937226054, 11274347, 814502780, 440383531, 143628108, 994157516, 583535841, 922692995, 336268058, 799300472, 112095752, 375430215, 655427444, 616096643, 259777366, 377184303, 891549279}

    3

    Returns: 22

  43. {605719969, 629829959, 637821154, 79967875, 671054618, 309975721, 622237909, 626794056, 632099045, 654706466, 618987493, 642260444, 302293879, 615577930, 605624052, 614131610, 612728061, 165015522, 604283679, 334129534, 306651048, 79061215, 20533209, 629088477, 323470673, 82272476, 632790651, 331969829, 324322316, 41276750, 331192504, 611354860, 331455571, 648638256, 162782297, 38964810, 635934567, 606997721, 659797456, 615599253, 19069997, 305708939, 620961879, 153495100, 634650540, 77157484, 665559266, 309824510, 317765596, 607313321}

    9

    Returns: 50

  44. {619551567, 189155820, 490815668, 771477356, 350073948, 29041951, 524418235, 5401329, 219541717, 52795552, 218959044, 167002176, 986849333, 809337529, 870802155, 310081607, 184604475, 492489466, 663566991, 551372596, 842855395, 690929197, 223436363, 29317746, 140482411, 480995938, 609635837, 817079984, 318134863, 145429732, 771951810, 401997786, 675338828, 401258049, 596914935, 481389852, 335738464, 793209413, 124667961, 837902565, 617272007, 438365694, 995767140, 345565921, 204358398, 230055864, 439688854, 870370301, 849203651, 933819137}

    26

    Returns: 5

  45. {910989356, 907352119, 913679561, 902902377, 466104917, 934189538, 879455340, 932711140, 226917419, 937837670, 934164376, 930611361, 28638033, 890253005, 938094665, 929318333, 898912335, 448179458, 939002231, 934489152, 882211167, 58635329, 915217112, 469046764, 463372421, 28278091, 910462623, 115717211, 912566963, 915075687, 460261287, 887666712, 927882757, 915347142, 897140093, 437824510, 899224921, 111228318, 900951121, 882006953, 917493343, 917128952, 233945014, 469287411, 894747080, 116430858, 218397864, 885857958, 228356539, 220030274}

    13

    Returns: 50

  46. {276104362, 625156823, 973229367, 872193200, 568731787, 934204775, 709926768, 284334033, 920278886, 145667254, 5955872, 548537171, 497797379, 791901656, 430895530, 158241259, 486120548, 922522404, 530553780, 364047759, 935704016, 381700141, 105831715, 628602227, 790884556, 870918601, 311351581, 890059276, 239355420, 217958924, 569908229, 390053647, 858406853, 405786700, 274351489, 990001009, 210956045, 875502366, 66244214, 241483112, 15244921, 368088151, 196836617, 577125991, 920013773, 43283211, 803652767, 818435877, 108445198, 625700752}

    783

    Returns: 0

  47. {213649581, 855511438, 854964042, 854985562, 427350261, 427713021, 53448652, 427544710, 53465216, 854818293, 854632217, 427756637, 427488449, 53432823, 427664103, 213758528, 854617985, 427787079, 854959335, 855613913, 427447743, 855429929, 855445304, 427560163, 427727382, 855440481, 427588591, 855544100, 213750162, 427381320, 854727696, 427458776, 427685499, 855097793, 855316781, 427365865, 854892852, 854995306, 213864157, 427568343, 854700856, 427735969, 427652056, 427411550, 855591420, 854597537, 854596489, 854920898, 855091675, 855131712}

    815

    Returns: 50

  48. {814942224, 649916341, 20232803, 461574172, 181309943, 747977271, 581438873, 955934188, 316699623, 816668726, 321050581, 166032801, 911049004, 200240848, 314789638, 30684920, 246429780, 333588066, 607688280, 598840556, 310904107, 564103817, 326929976, 913168829, 906349759, 295428129, 56521811, 539340005, 468041564, 532806473, 415623062, 607581987, 84550288, 86717276, 845969967, 41167987, 994667816, 989323000, 876201865, 338587154, 361456432, 638599162, 887491666, 940780670, 935768566, 830931839, 365719672, 91927923, 805224454, 770671587}

    9162

    Returns: 0

  49. {468148124, 936312528, 936186407, 468105097, 468183597, 468077259, 468079038, 936353730, 936307295, 468072259, 936287499, 936143503, 117015007, 234093738, 936312437, 468144066, 234076669, 936258429, 936261244, 468068094, 58518334, 936144978, 468147011, 936157489, 936160062, 936378002, 117026535, 117035408, 234050682, 468184222, 468138392, 936241880, 936285832, 936159220, 936319832, 468084030, 936287731, 936339405, 234035212, 936321083, 468121499, 936181298, 936292258, 936312662, 468092491, 936246531, 936132514, 468169491, 936294972, 29258709}

    3571

    Returns: 50

  50. {536291202, 294042849, 34431544, 730251497, 339579251, 573374363, 689647591, 318977619, 776874047, 884204454, 486806421, 544071129, 642080250, 672517480, 273502452, 854083969, 120360442, 353007238, 625514234, 518836879, 272565972, 423011302, 310343133, 818684809, 80163933, 742570411, 801060113, 177013299, 555246505, 239037243, 846243659, 842562962, 402050830, 295896891, 498218112, 367553516, 735462945, 849590672, 628589030, 853968069, 928968631, 223458655, 477002737, 315510499, 9540068, 526153997, 978590805, 691924042, 720741886, 699728446}

    21655

    Returns: 0

  51. {135348052, 541387477, 541389651, 270694851, 270694219, 541385391, 541387069, 135347780, 270695676, 270694514, 541390769, 541390231, 270696134, 541389667, 270696399, 270693404, 135347289, 541391143, 541387384, 270693685, 541386635, 16918383, 270694749, 541391930, 270694037, 541385146, 270693161, 541391592, 270696403, 541391658, 541386452, 135346260, 135347424, 33836568, 135347856, 541386167, 541390443, 541389960, 541389084, 541385741, 541388302, 270693637, 541388687, 541387619, 541385992, 270695999, 270694768, 541387571, 541389057, 541392684}

    66087

    Returns: 50

  52. {139474426, 576398225, 822921798, 566780078, 757352006, 455686856, 910566591, 141941085, 667842956, 32495682, 638237721, 849318942, 154388456, 996666604, 995465488, 818589309, 949654201, 448213236, 928337825, 808064840, 768440986, 782845381, 546341129, 685220491, 336294761, 424435214, 608829894, 89606036, 735069251, 574320570, 121199508, 420174576, 40337284, 253132792, 992042353, 675639403, 187002059, 508570932, 774250904, 248949522, 944881907, 667413786, 91184009, 620855091, 461883418, 278007961, 149024766, 572172379, 976632221, 812824029}

    721252

    Returns: 0

  53. {310060624, 77515156, 155030290, 310060653, 620121850, 620121963, 620121712, 310060631, 620121382, 620122081, 19378794, 620121691, 620121349, 310060594, 310060808, 620121760, 620121815, 620121169, 310060765, 38757595, 1211174, 620121560, 310060550, 620121585, 620121924, 620121934, 310060773, 310061013, 620121544, 155030401, 620121802, 310060799, 38757617, 620121736, 620121755, 620121328, 310061011, 38757607, 310060938, 310060959, 310060906, 77515155, 620121902, 310060884, 2422350, 310061019, 9689392, 620121099, 620121764, 620121717}

    605587

    Returns: 50

  54. {717202305, 645225161, 560586662, 740168304, 997161610, 494386647, 473384301, 143593865, 518492865, 148990591, 150426797, 573128877, 895374220, 266594166, 459066987, 552651826, 10896782, 293373615, 961021675, 375242669, 653444269, 469350753, 113586610, 980335603, 828775950, 205568512, 646500742, 592664856, 809262102, 846179393, 674980460, 368423026, 85305450, 733513497, 921424808, 772519574, 422877679, 160680637, 352902591, 603365720, 772832970, 821249187, 281828983, 839189966, 131373664, 665298815, 579224276, 671539789, 306706261, 300535622}

    1839950

    Returns: 0

  55. {822269519, 6423980, 205567399, 822269634, 411134757, 102783686, 822269644, 51391840, 411134835, 822269551, 822269522, 822269610, 411134789, 411134725, 411134819, 411134799, 51391853, 205567391, 822269628, 822269537, 411134843, 822269498, 411134760, 411134796, 822269523, 822269491, 822269592, 822269572, 411134760, 205567401, 205567387, 205567405, 411134764, 411134824, 102783697, 822269497, 205567396, 411134761, 411134818, 411134790, 822269609, 411134768, 411134754, 205567369, 411134764, 822269541, 205567399, 102783695, 822269688, 205567363}

    3211990

    Returns: 50

  56. {753810614, 94817436, 868693764, 638799016, 624281662, 176954637, 191949507, 31098501, 347754822, 939424091, 75257679, 425618420, 445050298, 154356547, 843005238, 398993746, 930956998, 6898624, 612360772, 618903614, 368129241, 260232977, 763346823, 871821715, 329821599, 898753714, 721423179, 258557808, 197604357, 165949793, 749631262, 44093232, 756260408, 325822234, 712459212, 994394993, 62776741, 91501338, 987214179, 101914640, 527974138, 219214815, 152168240, 357374505, 553008162, 354103589, 764338111, 239083035, 948227148, 691694569}

    11916738

    Returns: 0

  57. {624760838, 624760832, 312380417, 156190208, 624760837, 624760834, 624760837, 156190208, 312380419, 312380418, 624760835, 624760834, 312380416, 624760832, 156190209, 156190208, 624760833, 624760832, 624760832, 78095104, 624760832, 156190208, 156190209, 312380418, 312380418, 624760834, 624760838, 624760836, 624760833, 624760832, 624760834, 312380417, 312380416, 624760833, 624760837, 624760835, 312380418, 624760835, 156190208, 312380418, 312380419, 78095104, 312380419, 312380418, 78095104, 624760838, 78095104, 624760835, 624760838, 312380417}

    78095104

    Returns: 50

  58. {67492387, 905683583, 286422046, 802733055, 207496033, 382173301, 182200404, 487425074, 14756308, 787692863, 107020209, 551816660, 774952241, 537673442, 959447435, 851678859, 206029933, 897330340, 194214519, 203199290, 667152830, 617010442, 921530442, 261088775, 592699032, 636957143, 183215640, 351195735, 583372720, 43312147, 123792439, 740842702, 892627195, 749045760, 588499004, 797579603, 243654574, 612204838, 966124283, 354761994, 10106943, 981027399, 747760778, 262825048, 404117601, 404188522, 152954942, 908953826, 480966923, 364678100}

    351714774

    Returns: 0

  59. {780425928, 780425928, 195106482, 390212964, 195106482, 780425928, 780425931, 390212964, 780425931, 780425930, 780425929, 195106482, 780425928, 195106482, 780425929, 780425928, 195106482, 390212965, 390212965, 780425929, 780425931, 780425929, 780425930, 780425928, 390212964, 390212964, 390212964, 390212964, 780425929, 195106482, 780425929, 780425931, 780425929, 195106482, 390212964, 780425928, 195106482, 780425931, 780425929, 780425930, 390212965, 780425930, 390212964, 390212964, 195106482, 195106482, 195106482, 780425930, 780425929, 195106482}

    195106482

    Returns: 50

  60. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

    1

    Returns: 20

  61. {6, 14, 11, 3, 1 }

    3

    Returns: 3

  62. {3 }

    3

    Returns: 1

  63. {1 }

    1

    Returns: 1

  64. {14 }

    2

    Returns: 0

  65. {987654321, 1000000000, 998244353, 123456789, 999999999 }

    476

    Returns: 3

  66. {20 }

    20

    Returns: 1

  67. {9 }

    3

    Returns: 0

  68. {2, 2, 2, 2, 2, 2, 2, 2, 2 }

    1

    Returns: 9

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
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