Statistics

Problem Statement for "IdenticalBags"

Problem Statement

You are preparing for Halloween. You like to hand out bags of candy. In order to prevent arguments between the kids who get them, you want all bags to be identical.

You have a supply of various candy. Each element of candy is the number of pieces of a specific candy type. You want to create bags that will contain bagSize pieces of candy each. Compute and return the maximum number of identical bags you can make.

Definition

Class:
IdenticalBags
Method:
makeBags
Parameters:
long[], long
Returns:
long
Method signature:
long makeBags(long[] candy, long bagSize)
(be sure your method is public)

Constraints

  • candy will contain between 1 and 100 elements, inclusive.
  • Each element of candy will be between 1 and 10^18, inclusive.
  • bagSize will be between 1 and 10^18, inclusive.

Examples

  1. {10, 11, 12}

    3

    Returns: 10

    You can make 10 identical bags, each containing one candy of each type.

  2. {10, 11, 12, 1, 2, 3}

    3

    Returns: 10

    We have a few more candy types than in Example #0, but the optimal solution remained the same.

  3. {100}

    7

    Returns: 14

    This time you can make (100 div 7) bags, each containing 7 candies of the only type you have.

  4. {10000000000, 20000000000, 30000000000}

    6

    Returns: 10000000000

    Watch out for integer overflow.

  5. {1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000}

    1

    Returns: 1000000000000000000

  6. {1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000}

    3

    Returns: 1000000000000000000

  7. {1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000}

    1000000000000000000

    Returns: 100

  8. {1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000}

    101

    Returns: 500000000000000000

  9. {1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000}

    437433235

    Returns: 228606281231

  10. {999999999999999999, 999999999999999999, 999999999999999999, 999999999999999999, 999999999999999999}

    1000000000000000000

    Returns: 4

  11. {635958824641492470, 457523164253236435}

    489938305527970540

    Returns: 2

  12. {553854587011050798}

    507314301248389568

    Returns: 1

  13. {511875957488096693, 250327450451046281, 510192609857982438}

    8513403049400921

    Returns: 149

  14. {977120655296411406, 808569630277772075, 924534416041231092, 890281611472966354, 702186239842185083, 669295810359961713, 172170934909407959, 18348581702335137, 139448879767746963, 993097037486774850, 485449314289938635}

    856740329103337118

    Returns: 7

  15. {721471777908383332}

    44437121697049959

    Returns: 16

  16. {229068594266929173, 390189344393394673, 664130166000888055, 475956400122085840, 571311976160817858, 545303317453963860, 856004746570115823}

    682461966778426309

    Returns: 5

  17. {428493076956711454, 62533275745675489, 364623048039282593, 802009936952827925, 937177348608718380, 332633194892149392, 45453087389703171, 413223784656454735, 645018102914032309, 184887369134604294, 22771034598646416, 225350872905337546, 192276230352305894, 577486113203362152, 348554051542751681, 280738432890564362, 146745181560620368, 433685570680219103, 508404598515349093, 966281843835865262, 913701035230651098, 178404698756894406, 131085611547695098, 905898416908945270, 105403162126527695, 198556802997026045, 390077586535025623, 247703556286823918, 396780002286721457, 257344358725830819, 387641390186094243, 863423037666084154, 539112854526760602, 987839145349425104, 262962315309249393, 786977469180407695, 879686743941888538, 688374892060301185, 640793917782868021}

    496986740776582406

    Returns: 35

  18. {57954368504019747, 424212170980978062, 154278010426471361, 709428670559338610, 811165262103671752, 530853958370565832, 875039179018620400, 866970071246240806, 310243668856138329, 728266940386001329, 881981748393538182, 868120864128960153, 865172292269525994, 948049004984824871, 783374004495138492, 142585055001293047, 307859345516801707, 993758836028932756, 147138755344847055, 888403840747935077, 723748454126199604, 345585796880469437, 782999739345203853, 597342528296486524, 636162179045908537, 621887138761243999, 803652071268433019, 843177355923922230, 866832691756570159, 104904719287231168, 623608260651666947, 56474161049121992, 484803428418258261}

    705581103078412119

    Returns: 28

  19. {5724629265117926, 366679331940943423, 992480686720325561, 398199252386720692, 526396011353446667, 35064047591862417, 386597513356789085, 925873059431622395, 582494026021001013, 264243411095135428, 108573916424713827, 284583489014662103, 683462438209481875, 439323185538271094, 372105262745978481, 928580452563058862, 301626065267520086, 716497569802712064, 174914097958014648, 717222764050604479, 592995340754636398, 518266003517656721, 878105719393632101, 253919215084188511, 314092005110952411, 172113471851261746, 375478047680617243, 946290525811524054, 303762732900840842, 632827234773560111, 205417476059685605, 868377780234406133, 232540870226288202, 206542461968582955, 689071139809211729, 526353867088046890, 298460245349278958, 544895483446851108, 895135520126629916, 115146551790546092, 322633272762993923, 652810251966406159, 717309432422643808, 138425613911881168, 188989440528757859, 32314794440804013, 31161529362442749, 369497205101940746, 375956752700172491, 301794413423899383, 214514883678171045, 183028741600099225, 922891645184909432, 329834383698129888, 150667632825107844, 915369300096870260, 453318248292345506, 624955162890101123, 138049035498967168, 185620424773444701, 714019217699501642, 715672645337727671, 119375833972801216}

    283079735907381276

    Returns: 97

  20. {673072021903636665, 216491750142331310, 918508311402472235, 699331008308179528, 505873599851398312, 559290832537627535, 648030516711597237, 121902598796985352, 983489064521168840, 900459298190488129, 201404787196792500, 435997576951030130, 540721618932924579, 790772313460874201, 575575413048466696, 473886581829511762, 531221328978440041, 261353035096594513, 984072566693307755, 433804539644035712, 851917023332748301, 298560015093225663, 259041357810561158, 167955852037263686, 213511663860664963, 742840363608580310, 878277063086903412, 423315440016550823, 339784253568765097, 77537744027766224, 588334958468783115, 690733735477057395, 589234089912564785, 807271236758513022, 242739838895299962, 449300431318754914, 982370457012372914, 571269230711915176, 368692248821670674, 25474407859716768, 408077390787889828, 731122543909552270, 858959580469978420, 287246280861096387, 928199215881876194, 942159197761244614, 152434951707945050, 624281213030569569, 863485284857713718, 584300469315720809, 567205904473911058, 698780333829182030, 406001183458414310, 469064442861282399, 107326919110447472, 459852843997906088, 165082439374465643, 49889607342449321, 937061072495699227, 12634672202840780, 955296729601500506, 633342216912470605, 206233713760603065, 629236476657389164, 371341924855139285, 881588651307421048, 344268117518197827, 34491929008423333, 609427791198212933, 261832707479693162, 31325483298394934, 107263247015924591, 111053052035999734, 117020324262069145, 218566349216211343, 530561016764734632, 128616503158141404, 561501845985074301, 336054390747560061, 987089847465675766, 959391705972035004, 924986099732551165, 724844363205652644, 10025151322916225, 745669901098559141}

    190996405850904189

    Returns: 223

  21. {649305639831290324, 575118228121375093, 361834586733971347, 424291090992944557, 445107611528905032, 341738264471986407, 412799578501250097, 383964707173619683, 686935048397776429, 901202922973597410, 266170159654014375}

    397856395928615824

    Returns: 13

  22. {364956587583360921, 8597722275404844, 734961881611282924, 393331279495064738, 208980072854122092, 254358348789758678, 469844632935404250, 188342885918425231, 798520805134283895, 490045294618645782, 442615076674717573, 100378014051428138, 440242956039617949, 537555983670085234, 210673085907174250, 962343174848803902, 243539405947445481, 136995569946383154, 557782065374438859, 586248861855407200, 45209511213646556, 822818621687450583, 252846427850890339, 337968902863501812, 32875258432402254}

    428029170973802655

    Returns: 22

  23. {197697029586058104, 720625343533306342, 972052588743084423, 682044779286722722, 981752004182155198, 300568354824198546, 127097215069709130, 327022908133309697, 301248327444682736, 831779338389525104, 862595535499949335, 174229020221132878, 76278868205796272, 946370978234697805}

    168548005525362092

    Returns: 44

  24. {324806230275869760, 935956085199937611, 900234202450035621, 855586694128346646, 724466134770520079, 984598236954725413, 536176982325665113, 331732289048725084}

    286151581271374452

    Returns: 19

  25. {937446307226411115, 31631589935553552, 3676129020886872, 28024114645790879, 50104019158810742, 306308597199096931, 756237403603766570, 385024336593619425, 32426987598931821, 495030689549969230, 437352997517760102, 545620321899350882, 517966478741549969, 590259501730782332, 658297521103553207, 868852685806171564, 305684739494948385, 139480812573232811, 702870442483964018, 881373255490583156, 276377275427429485, 491145786642446758, 600462652331981128, 546599303867803099, 684562572733098030, 457638893880913694, 749015606845393327, 859957011350339727, 76968583374762736, 831373751802620375, 57718957336580202, 924191576362294661, 944076615277669859, 869070061258231759, 816577949482137065, 66856967267660582, 939573580924409477, 503596058395923991, 442719269654966293, 420376956530878353, 36762750261441485, 229088215962190919, 751938843789139205, 911963509826576565, 577767411925745758, 860183294472853221, 591453820640720411, 204080345321572304, 164452012865481933, 902982936797159394, 185152264015926099, 87044725431745358, 486789402926143827, 9439751970547196, 332766781617453867, 526384268326500691, 31411206542229048, 862461594713637076, 126874923386614817, 65496864439140783, 638365592643047200, 147799036678002788, 322908121844235061, 592841232563083148, 585301426762023574, 916206371225312358, 641176832956550362, 455506171807290785, 108843428025185934, 752793523103785217, 827935324164067322, 165003588355860058, 865747146773360822, 581690574159845630, 289518634007586859, 674660758752054462, 710404165663237135, 95087612939874748, 757981146830884022, 944151058785831041, 285923410246933329, 897073008192804151, 504769614202746671, 901732632995054825, 882021825225991464, 975724530355763178, 54755546930504174, 28296885592808292, 289172160819798728, 847707139937649908}

    243331972855874136

    Returns: 184

  26. {3975511780, 729417119757}

    16387441

    Returns: 44753

  27. {1, 351233797, 97235, 1852383, 1386210215, 27679463, 432326910629631624, 10478278137934, 114894953446, 10214, 793626865, 7, 22910604931, 140155494, 288336358970660964, 99228342094}

    633812781409687614

    Returns: 1

  28. {28988947893384, 16023360405371}

    8065418031550122

    Returns: 0

  29. {390, 606350355362}

    383530036435721615

    Returns: 0

  30. {201816457482550, 99, 1, 16058064932750607, 22052, 42143431559821, 9007459, 16985205744562979, 24719426684527626, 7, 26028719664718430, 3577, 700000864, 15402, 15796}

    9395148784183

    Returns: 8944

  31. {1}

    677517204902938097

    Returns: 0

  32. {760, 415892573362037371, 807338, 15522785735746496, 282429243926059760}

    3

    Returns: 207946286681018685

  33. {48549331205953132, 1, 4, 8, 180909204062, 194227, 96084003446, 874980777797}

    22614405079200

    Returns: 2146

  34. {14, 19974204, 27, 114, 8287233915027008, 682064775, 255710472, 5, 39147258, 288716403012315757, 3, 2}

    6753490

    Returns: 43977798644

  35. {5883103, 7329570776, 144371299591}

    14

    Returns: 10312235685

  36. {1911242, 4971, 31167, 43668, 28150, 5445336968579438, 279298449, 66258586961, 52, 416371252699459919, 65950189491386, 29436, 448983619369558, 1313948964964, 25260}

    2660692

    Returns: 158730333730

  37. {216085679305402227}

    11459

    Returns: 18857289406178

  38. {46247}

    2568958

    Returns: 0

  39. {8156, 1022689411513, 3984426282880, 76, 5, 32766891266387689, 2106853961556970, 27632, 59, 1654117086546, 39030417853424, 401, 81445165, 947175, 90423922, 23351, 173043261312292029, 232064039876, 7095757285, 3, 1519906647132, 68, 77656328, 49092, 5297, 211052, 997, 588344238, 449412, 3786263315652357, 1682625810655, 4, 16826019360, 121488150604248, 239664195, 425458106946801, 6301249, 20294205091438172, 111205605533398004, 2936, 40585654, 3955077628061280, 191960208450, 82368, 211772909703703, 353, 740401005339, 34, 126098, 375, 4546542, 955688, 703772418245, 1043603406, 188938187022409266, 4713817, 659110, 793543113130, 23344239, 84302, 5, 652548, 6673175037857, 216, 397465097, 41027949279739586, 64, 5, 925388423133463741, 2, 26723631, 31, 7612865, 132221037, 194741090051771421, 2, 56, 4, 10252226, 3302245418}

    5477008

    Returns: 310035514531

  40. {107511501409, 8}

    853701333845837895

    Returns: 0

  41. {1592409131, 1488868312549, 99421}

    643616960385

    Returns: 2

  42. {967, 2, 107916767, 3667902499, 203274, 4045549445098702, 157627145608545956, 18, 117549781466, 245302733170, 447691886957, 594784784766, 7132953003296881, 18810, 28712685220818, 49047994059346, 3490630478323, 774681412, 866973196984685, 15939948877499756, 175776628820283, 907, 20098059585991661, 15107, 800974, 1377735987, 51898695, 3984112}

    249271679150384

    Returns: 826

  43. {3746986, 2011, 64236930115, 358098868543014775}

    1450639979

    Returns: 246855827

  44. {15529424393}

    95410190623038

    Returns: 0

  45. {124467, 884, 478}

    45294364

    Returns: 0

  46. {901757087637, 214, 45646480214401}

    78

    Returns: 592811431355

  47. {35495682058190}

    1004744907798256

    Returns: 0

  48. {23368186919, 73668, 21674711, 1267522965, 3671, 9968623150, 193865520654038144, 20325073484038, 8774, 2542204979958, 35, 57737968017, 25985557435, 129956822595169478, 67086186, 3202, 71080812990808912, 61786, 392680012350, 739920, 650779255932, 333, 4901814997, 37727420451727297, 4488707245, 5, 4306, 129705189, 64039511290723, 9, 15, 1533650871568, 57, 443, 361465346432593, 1352966135626, 2893079257, 5226688959, 38545690, 480587453, 101397, 133848470732442, 7207502372969, 13688751724, 490153181, 47220005543, 59288495, 8158898349554, 3518423876857736, 17731780, 183472460, 341922, 1, 4441428, 46933640247, 471, 319564727328093991, 343, 1475990888, 29920027592841, 313324148153}

    29982634

    Returns: 25226114983

  49. {93, 35593941221, 7955606162}

    650

    Returns: 66905904

  50. {1284457052349, 453422219195792, 24776317630, 189617960911154, 6924135510719219, 5, 27748223781, 864269662, 59924, 72767406838735, 2188586990025094, 1, 143032613380, 1545, 5934825422, 6359701, 5, 2363, 62786988490621767, 475589703, 1275, 17198, 102876, 14}

    1

    Returns: 62786988490621767

  51. {688630284119051292}

    1604

    Returns: 429320626009383

  52. {28, 33, 26, 30, 34, 629388226185897, 32, 28, 28, 6923270488044637, 21, 62938822618587323, 18, 34, 24, 6293882261858756, 25, 629388226185873020, 28, 24, 12587764523717481}

    1142

    Returns: 629388226185873

  53. {774002455420701463}

    595111837168

    Returns: 1300600

  54. {47707792193606059, 940129408479637, 51444500617540653, 519590344347349844, 987350306771964, 481763533305727}

    132817688

    Returns: 4676725591

  55. {976868763845620685, 976868763845620689, 57, 62, 52, 97686876384562113}

    21

    Returns: 97686876384562068

  56. {615045406841417661, 786943342425916181, 408956256526384579}

    9481387464888577

    Returns: 191

  57. {93646747608000006, 7803895634006, 9, 78038956340003, 780389563405, 7803895644, 5, 1560779126803, 7803895634000014, 8, 7803895634000006, 5, 85842851981, 6, 7803903437895641, 7803895634000006, 7803895634005, 10, 78038956340010, 6, 780389563400000005, 78038956340010, 78038956345, 78038956340000007, 780397375099529639, 6, 3, 9, 6, 7803895643, 78038956340005, 156093520471278, 7803895640, 7803895634007, 780389563412, 4, 780389563409}

    226064528

    Returns: 7803895634

  58. {905979660998719178}

    905979660998718182

    Returns: 1

  59. {70554431142600031, 71189491507527794, 69787474467798, 69863612538904400, 69793755277660041, 767654542600036, 76835241036637, 697869161735574, 698565634463867812, 6978677660035, 837442714935555, 1465661882153233, 139594489232980035, 7188037989830}

    1609890708

    Returns: 697867766

  60. {598737045, 658610700038, 598737000000034, 59873700000000031, 34, 5987370000598789, 65861129874298774, 30, 120346137000000036, 5987403, 599335796873700038, 59933580286144, 658610700031, 59873700598773, 6586150, 659808233873700043, 599347711774, 49, 59873700598772, 59873700598737031, 59873705987401, 598737000029, 598796879687412, 5987400, 598737000000029, 59873700005987404}

    2727404703096

    Returns: 598737

  61. {6, 600000011, 6000000008, 60000000011, 12, 60000000000071, 6000000000000609, 9, 66000000000000010, 60000006000000014, 11, 6010, 6000000000011, 60000060000000016, 19, 60000006014, 9, 8, 600000010, 17, 8, 9, 600000600000000013, 9, 6, 600000009, 600606011, 600000000016, 13, 9, 6000000006018, 600000009, 12, 16, 600008, 600000000000012, 60000000000000018, 600000012, 20, 6000000000016, 15, 9, 6000000000015, 11, 60000000000014, 6000000014, 6000016, 6000000011, 60000060000000010, 11, 600000008, 11, 600000000000000014, 8, 13, 6000000000013, 10, 6000000069, 12, 6000600000012, 11, 6000000000000013, 6000000000008, 11, 6, 60000000000015, 11, 60000000000000012, 17, 6000600009, 60000000006000007, 600670, 60000000010, 10, 600008, 6000000000010, 12, 66000000016, 600006000000008, 16, 16, 6000000000613, 60000000000017, 600000009, 13}

    273249268902504333

    Returns: 6

  62. {664356096204731144, 332178048102365721}

    30

    Returns: 33217804810236557

  63. {975808752194131940}

    7683533481843558

    Returns: 127

  64. {5000550000000022, 500000000513, 5050550000000012, 5051000000000010, 9, 5050000060500063, 16, 550500000000011, 500000050500010, 50000050000511, 500005000500017, 73, 500000000061, 505500000550000015, 50000050000009, 5000000010, 5500000000000008, 505100000000000013, 50000000000000017, 500050000005511, 50050000014, 550000000510, 5005050000007, 500000000000014, 50000000513, 50000000063, 5500000000060, 5000000062, 500510, 500000050000059}

    217882974182401676

    Returns: 5

  65. {62330686655589426, 612294377747484960, 60623750890286215, 110179950528122202, 12774487017753425, 110785637412584647}

    17598

    Returns: 55062444042040

  66. {186305591475384065, 22481980375862396, 22113423320520387, 591718352351590657, 187964098224423077, 184462806198674029}

    6485

    Returns: 184278527671003

  67. {6, 9106, 2, 94, 9, 91910000000002, 91910000910001, 6, 6, 9100000000004, 91000000000914, 9109100006, 91006, 5, 6, 9109100000003, 10010000003, 91005, 9100000000006, 8, 7, 910000004, 4, 9191000000000009, 5, 91000000000000010, 91018200910005, 6, 5, 4, 91000000000005, 2, 91000000091005, 3, 3, 91000000000000092, 5, 910000000004, 95, 910000000910000004, 910000000910005, 4, 2, 91005, 910000000000910007, 3, 12, 91000009, 9, 9, 910000005, 9100008, 3, 10017, 3, 7, 9100000009100006, 9, 8, 910009100008, 6, 4, 3, 6, 91007, 9100000000006, 9100005, 9109106, 910000005, 9100000000091004, 99, 91000000000000098, 8, 8, 5, 91000000000000009, 9191000102, 6, 6, 5, 9111, 3, 5, 10014}

    24317440652646536

    Returns: 91

  68. {5618978791233, 510863207642618947, 5108167691972702, 510811610510811691, 618133180342161089, 561892827700088798, 102218618598619356, 510826934399381245, 510969961650181231, 51132242773974003}

    66207625357

    Returns: 51081161

  69. {31775772775775, 635514820000000029, 3527107251000032, 31776058757410029, 31782096148228, 318106943151000035, 638692394417757443, 63869239441, 3527139344498436, 29, 31779236331541, 318106943151000034, 31785591479741}

    61348013651

    Returns: 31775741

  70. {192403577240350193, 808516947274981246, 186217625402130, 62108321461903687, 62045655350183}

    171370115

    Returns: 6204565535

  71. {49335, 49320000012, 991332054252000014, 49320000054266, 493205425200000013, 493200049328, 49320000020, 493200000000000007, 14796049334, 493200049320000006, 49813213, 4932000000010, 99133200012, 7, 493742524932547462, 493200000000004950, 4932000049327, 13, 14, 498181324946, 54252000000000010, 18, 4941, 4981320049813211, 54252000054267, 986400000016, 493200049320000012, 493249325425211, 4932004946, 12}

    813244587131477

    Returns: 4932

  72. {58, 62, 81, 52, 55, 64, 80, 574905011791171485, 44, 69, 65, 47}

    1

    Returns: 574905011791171485

  73. {100189721052917585, 10, 11, 13, 11, 9, 11, 21, 15, 10, 8, 6, 15, 711893931004197, 11, 10, 7118939310041842, 13, 15, 15, 15, 15, 14, 11, 21, 12, 18, 711893931004195, 21, 19, 20, 12, 12, 711893931004194, 71189393100418311, 15, 13, 15, 711893931004192, 14, 22, 10, 711893931004198, 13, 8, 12, 14, 20, 71189393100418311, 711893931004183010, 15, 21, 8, 10, 17, 10, 71189393100418313, 7118939310041839, 13, 10}

    1325

    Returns: 782732195725918

  74. {9558154, 111, 16, 811048781954458441, 18557, 1, 26, 24, 27, 30, 740573764831805897, 30, 37, 17}

    1

    Returns: 811048781954458441

  75. {371021, 12, 14, 14, 10, 16, 8, 15, 8940799881518911, 8940799881518906, 13, 13, 13, 14, 23, 15, 8940799881518906, 10, 8940799881518905, 89407998815188965, 8, 8940799881518908, 12, 8940799881518909, 894079988151889613, 89407998815188975, 13, 11, 10, 89407998815188973, 89407998815188976, 7, 20, 89407998815188982, 13, 14, 9, 9, 16, 14, 8, 8}

    156

    Returns: 8940799881518896

  76. {3742703754824311, 17647444496417541, 5553461621, 18428116884, 458448759, 444567908269059, 802653166838033042}

    16

    Returns: 50165822927377065

  77. {7793667028774, 126729927591029, 701779, 240043493530916734, 69605291704472645, 8098936802504, 49138580717699708, 971469799295, 13134, 188268718155000058, 896517705500054, 179303541100000044, 17930354110060, 65, 905482882555073, 898310740911000054, 89651770550000051, 896517705500062, 89651770550000051, 90548288255500070}

    171603

    Returns: 11056307564410

  78. {31, 640317725952, 128063545187200017, 9, 17, 14, 640317725936010, 18, 13, 16, 64672090319536013, 64095804366193611, 64031772593600011, 640317725954, 640317725936007, 640317725954, 13, 20, 1280635451872012, 15, 16, 704989816255536013, 640317725936000018, 13, 20, 64672090319536016, 640317725936012, 6403177259375, 640317725950, 23}

    2708114

    Returns: 640317725936

  79. {1041008586255, 617348319606390087, 11230915353125123}

    5603246

    Returns: 112181429967

  80. {84130, 530295726333731710, 36537, 4661025949, 978370522701, 136447842885060, 183106394, 774062531627929724, 238173086654747763}

    17

    Returns: 86006947958658858

  81. {41897525368387252, 5637302400618289, 564285520283264710, 36488130134117, 308598580127049082, 900304646308614, 58896634244273}

    31359805042488

    Returns: 29382

  82. {3, 664529, 1971, 639431793012, 638793023, 63885751809300021, 24, 63879300012, 70267868793034, 638808, 12, 63879300000000025, 63879300014, 21, 16, 63943179301277612, 17, 6387930020, 63879300000000020, 6387930018, 20, 63879364524480953, 6387930000015, 14, 70267868793000020, 6387942775860022, 6387955, 127758600000018, 6387948, 63879300000024, 6387930000027, 638793006387930027, 22, 638793017, 63879300000000024, 25, 63879300022, 63885694317930025, 63879300014, 24, 18, 639431823, 6387993879300023, 12776498793013, 17, 63879300000000014, 63879938812, 15, 17, 7026723019}

    1930572878035

    Returns: 638793

  83. {3711524791308249, 7751830516244054, 172, 2660236921, 1689, 4935759810684751, 461610795, 6072000300093100, 330060330000300078, 993060000300006078, 336330000030360088, 60003000306030373, 30030000000939064}

    585185110312576126

    Returns: 3

  84. {190711395, 27918988, 128369996891692, 4118965218516, 411899954378218525, 343218843904937017, 34321850000016, 343218500000000020, 3439049713218525, 3779556443875, 343253165068500015, 724225356850000021, 72076228252821871, 3432528218500025, 3500832132185022, 3466506850000019, 34322193218521, 343218877540350027, 343252821850000020}

    856095812820

    Returns: 3432334

  85. {4048405360518, 45995, 431902, 28, 447378982227132, 8947579644542034, 4473789822271029, 25, 492116880449810026, 38, 5368547786725230, 903705544098742031, 456326561871689, 447378982227100039, 89927649217469399, 4921168804498136, 42, 4482737401915567, 49659067027208137, 451852772049400, 45, 29, 8947579644573, 492564259432037131}

    559908

    Returns: 4473789822271

  86. {68136910311945, 97012, 4, 970000000009, 97000000000005, 194000000000000009, 970979700000014, 97000000000011, 16, 9797970106, 970000000008, 9710, 97011, 97000009797000005, 194000000000000006, 970000009700970011, 97014, 10, 9797000011, 9700000000012, 9700970008, 194000000000015, 97000000000010, 970009, 15, 97000000000010, 10, 8, 194009700000013, 970000000970011, 97000000000970011, 194000000011, 97970000000011, 9797979708, 970000009708, 970000116409, 97000013, 1940000000000010, 97000008, 97000005, 10, 9700009}

    16049162807174501

    Returns: 97

  87. {1465739487771, 313, 68119431900504, 48544257, 3381, 1307, 255220378788910, 298532732565, 13200060000060147, 66066066012120669, 66126060006060667, 12666600000660073, 780606120006060070, 12660060012660073, 60066120618060065}

    168565181109280216

    Returns: 6

  88. {3326083752470694, 762499, 120, 944051, 23402, 15320799655334, 138062706, 353330580869331, 16290900, 61322, 9, 6, 8, 5, 6, 5, 13, 9, 7, 14, 11, 5, 5, 8, 69058610834203513, 7, 7, 690586108342035004, 690586108342044, 5, 8, 5, 690586108342040, 6, 8, 10, 69058610834203503, 12, 6, 8, 9, 9, 6, 11, 1381172216684075, 6, 7, 9, 6, 10, 5, 3, 5, 7, 690586108342042, 9, 6, 5, 7, 69058610834203504, 6, 8, 7, 12, 4, 6, 6905861083420356, 7, 6, 9, 690586108342040, 6, 9, 690586108342039, 11, 690586108342045, 4, 2, 7, 9, 1, 5, 69058610834203504, 7, 8, 2, 759644719176238505}

    2518

    Returns: 690586108342035

  89. {28778, 651090000065145, 651090651090065145, 13028961990065144, 195327664308429212, 716199723492510219, 664762890035, 651155239869090039, 65831716411551122, 130218657602853294, 65109065831709950, 65760135, 651155825850090046, 13021800065109038, 71692242610160471}

    49524386858197

    Returns: 65109

  90. {178102518421848169, 33346426, 23, 846101890147947825, 17, 29, 29, 18, 84610189014794803, 27}

    110

    Returns: 9954139884093503

  91. {6225287780457436, 595349, 23380545708, 773123217220568530}

    8501

    Returns: 91667443350790

  92. {32140, 87, 39, 3414305642, 2357290514, 786730, 29348, 698, 2, 3031226357, 18113475468027058, 27093732577071652, 11787700434, 189064006921977, 9098144011373671, 909011669626231376, 917928946221671659}

    20908911986

    Returns: 89982446

  93. {104274621348420660, 4, 9008054, 8295140333927, 3, 2675820339, 2814, 99112554929966, 192493759793, 337207222309593732, 259398530700042, 521593070000000035, 261963700000000030, 2593700038, 259370003115033742, 259655309855663736, 259370028530700046, 261963702593700035, 259655335530729, 259655309593748, 259370000005187437}

    933520356317

    Returns: 2705515

  94. {162113270024989465, 55841329007846, 93, 5, 8593594551209642, 4, 8, 859359455120964006, 8, 859359455120967, 1, 2, 3, 5, 6, 7, 12, 3, 8593594551209644, 7, 859359455120964002, 2, 2, 5, 859359455120970, 7, 5, 2, 4, 3, 7, 4, 7, 7, 3, 859359455120973, 859359455120964005, 7, 6, 7, 5, 5, 1, 859359455120964005, 2, 4, 859359455120964002, 7, 1, 9, 5, 7, 2, 859359455120964006, 8, 3, 6, 2, 11, 5, 7, 6, 4, 10, 7, 6, 6, 5, 5, 859359455120964008, 6, 7, 3, 7, 7, 8, 7, 2, 8, 6, 4, 6, 8593594551209646, 6, 10, 859359455120970, 3, 7, 3, 8593594551209645, 85935945512096405, 5}

    7144

    Returns: 880491245000987

  95. {1998009333, 61431016, 5212445880472, 833448617934261396}

    184636379693013

    Returns: 4514

  96. {1}

    1

    Returns: 1

  97. {1}

    2

    Returns: 0

  98. {10000000000, 20000000000, 30000000000 }

    6

    Returns: 10000000000

  99. {4, 6 }

    5

    Returns: 2

  100. {5, 5 }

    10

    Returns: 1

  101. {5 }

    6

    Returns: 0

  102. {1, 3 }

    2

    Returns: 1

  103. {10, 11, 12, 1, 2, 3, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 10000000000000000, 432143214, 4321432141241, 432143214, 432143214124, 324, 4321, 432, 4231, 432, 4, 324, 2314, 2134, 231, 4321, 4, 242342314231412 }

    43242341

    Returns: 485872055311

  104. {10 }

    20

    Returns: 0

  105. {1 }

    1000000000000000000

    Returns: 0

  106. {1000000000000000000 }

    1000000000000000000

    Returns: 1

  107. {1 }

    2

    Returns: 0

  108. {1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000 }

    1

    Returns: 1000000000000000000

  109. {1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000 }

    10

    Returns: 1000000000000000000

  110. {1000000000000000000, 1000000000000000000 }

    1000000000000000000

    Returns: 2

  111. {4, 6 }

    3

    Returns: 3

  112. {1, 1, 1 }

    100

    Returns: 0

  113. {5 }

    10

    Returns: 0

  114. {1 }

    100

    Returns: 0

  115. {1 }

    6

    Returns: 0

  116. {100, 200 }

    4

    Returns: 66

  117. {10 }

    100

    Returns: 0

  118. {1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000, 1000000000000000000 }

    7

    Returns: 1000000000000000000

  119. {8589934592, 8589934592 }

    8589934592

    Returns: 2

  120. {200, 2, 1 }

    2

    Returns: 100

  121. {1, 3, 7, 12 }

    3

    Returns: 6

  122. {1, 1 }

    3

    Returns: 0

  123. {1 }

    111

    Returns: 0

  124. {1, 100 }

    2

    Returns: 50

  125. {1 }

    10

    Returns: 0

  126. {1, 38219, 13231298, 12389321, 21893218, 128321 }

    312

    Returns: 152036

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.
This problem was used for: