Statistics

Problem Statement for "CompilingDecksWithJokers"

Problem Statement

You are given a int[] cards, the i-th element of which is the number of cards you have of type i, and an int jokers, the number of jokers you have. You want to construct decks using these cards. There are two types of valid decks:

  1. A deck containing exactly 1 card of each type, and no jokers.
  2. A deck containing exactly 1 card of each type except one, and exactly 1 joker.
For example, if there are 3 types of cards, the following four decks would be valid: {1, 2, 3}, {J, 2, 3}, {1, J, 3}, {1, 2, J}. Return the maximum possible number of valid decks you can construct with the given cards. Each card can only be a member of a single deck.

Definition

Class:
CompilingDecksWithJokers
Method:
maxCompleteDecks
Parameters:
int[], int
Returns:
int
Method signature:
int maxCompleteDecks(int[] cards, int jokers)
(be sure your method is public)

Notes

  • The total number of types of cards is equal to the total number of elements in cards.

Constraints

  • cards will contain between 1 and 50 elements, inclusive.
  • Each element of cards will be between 0 and 500,000,000, inclusive.
  • jokers will be between 0 and 500,000,000, inclusive.

Examples

  1. {10, 15}

    3

    Returns: 13

    10 full decks without jokers and 3 decks with jokers instead of cards of the first type can be compiled.

  2. {1, 2, 3}

    4

    Returns: 3

    Three decks with one joker each can be compiled: one with the card of the second type changed to joker and two with the card of the first type replaced by joker.

  3. {1}

    5

    Returns: 6

    Note that a deck can be composed of 1 sole joker if there is only 1 type of card.

  4. {2, 3, 4, 5, 6}

    4

    Returns: 4

  5. {123, 76, 117, 59}

    89

    Returns: 112

  6. {1000}

    1000

    Returns: 2000

  7. {500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000,500000000}

    500000000

    Returns: 510000000

  8. {1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000,1000}

    1000

    Returns: 1020

  9. {226122832,189005257,189156969,236469917,256021284,198044647,205010994,248049174,178890212,179064641,205487139,181900883,219085859,194404080,180119514,175328654,176680847,219902799,214484673,226685686,184943334,244938159,226671718,232300525,217741358,198257030,182016553,218493681,210887836,254883164,233331681,196181103,181327118,185685373,189721110,208014083,188970297,214101097,211243656,226812722,245703580,236080919,200802807,189449256,236569874,187225989,233477105,187225898,204877564,176866378}

    150562962

    Returns: 191896735

  10. {127490265,131350675,127055297,127381463,129728253,129769197,130054235,131490848,126676483,128992029,129344019,129075751,127871041,125966312,131069111,131017321,131724623,127822714,126558220,131406680,127104487,131512075,127908054,129985109,126776004,130873382,130416930,129521658,131121732,129651155,126665720,132095055,129405544,127593091,128962469,127124470,127839697,130567731,129610791,128931675,129840068,129660562,129735329,126880153,126365408,128155917,131013958,130050586,128156413,125995706}

    307811391

    Returns: 131649910

  11. {397157650,401763389,377539577,382674971,409157007,350626705,391704216,376731407,429871158,422479397,384109904,360087755,406847761,339825184,348395178,360308857,350252980,415483110,410340562,377821676,380857829,410044716,432419527,365303240,373796197,343600730,350762028,383767361,359621086,370668226,422236301,367721016,377683186,421459044,417019420,415631229,347593161,397119051,353205700,378240715,336531190,343196302,402810367,370406824,374699564,345629280,423260198,347851277,385662711,431488090}

    209929623

    Returns: 363161135

  12. {288414605,249535639,265085490,249855079,114768747,160773068,230462420,125402273,158004624,128232675,83674890,104824240,223016818,158066994,106001106,141704808,292468649,211120042,138775770,100585989,250173419,282988145,177324768,242301648,102709616,221539988,181208043,93270699,125701670,218437878,214876042,104245589,125943255,231228521,188913227,109173310,279584494,218986278,254659547,178744013,238973967,144766106,120739747,252601293,181866574,282716215,183027159,144582742,230079542,102724496}

    237188236

    Returns: 113401241

  13. {209774944,293946777,316822315,181018667,145186229,224492093,272083203,192705843,226577257,215805665,174187722,222038443,301884072,223208726,142773929,190200452,205403967,323157462,192842678,265437535,193927228,131569912,277825888,236306011,122924277,244295593,325779930,186992275,162663740,226970846,323793307,326989652,231005652,304486798,199534279,226469133,131620501,273482487,177676671,227116288,324803591,163312572,295207875,263944811,179210189,290773049,140639012,274981149,304089725,234177510}

    301071063

    Returns: 162896266

  14. {2,0,4,0,3,4,2,4,1,5,1,5,3,4,1,0,0,3,5,0,3,2,1,4,3,0,4,5,0,3,0,5,5,1,2,4,5,4,3,0,5,3,1,0,4,2,0,3,3,3}

    76

    Returns: 0

  15. {4,2,2,3,3,3,2,1,4,4,2,3,1,1,1,2,4,4,1,1,3,4,4,1,4,3,4,4,3,3,2,2,3,1,4,3,4,1,3,3,2,4,2,1,1,2,4,3,3,4}

    18

    Returns: 1

  16. {4,1,3,3,3,2,3,2,1,3,2,4,3,1,2,3,1,2,2,4,4,1,1,1,1,1,2,4,3,2,2,3,1,4,1,2,2,1,2,4,4,3,2,2,2,4,1,2,1,1}

    15

    Returns: 1

  17. {1,3,3,1,2,3,1,3,4,2,4,2,4,1,2,1,1,4,4,3,2,1,4,1,4,3,3,2,1,4,3,2,2,4,3,3,2,3,2,3,4,2,4,1,1,3,1,4,4,4}

    13

    Returns: 1

  18. {2,2,3}

    4

    Returns: 3

  19. {2,2,4}

    3

    Returns: 3

  20. {2,2,4}

    5

    Returns: 4

  21. {100011,100007,100017,100002,100006,100006,100017,100008,100001,100011,100017,100012,100010,100000,100004,100005,100017,100015,100016,100002,100014,100001,100005,100014,100011,100006,100015,100005,100006,100010,100009,100007,100016,100004,100003,100002,100017,100000,100016,100012,100007,100015,100009,100002,100002,100009,100001,100000,100006,100017}

    18

    Returns: 100002

  22. {123, 1, 117, 59}

    112

    Returns: 60

  23. {72758362,212587823,301878381,451868829,419074050,267428994,161862087,44749444,293029662,444733919,354441902,407043072,442865955,293877114,222393384,337756703,188134334,191465061,166093226,286040587,178342222,73429757,306115229,39263870,48811625,194610556,503522,29463368,373862487,276906089,365681222,68866761,90951059,332365344,472331027,56043135,148882766,415877458,282100099,143644527,273972203,85612165,128248131}

    162364615

    Returns: 29966890

  24. {71374736,183246581,465707283,250757476,487592230,429226927,265955904,77010571,64849987,393826940,229448607,260035883,161724,462955484,79607454,422485554,71883965,458922557,87769405,354959286,200946241,352578182,426853272,426962826,55631258}

    165310340

    Returns: 55792982

  25. {369096882,364629999,263620532,324512826,247393767,233076917,288933670,75313813,366433555,2626617,18089890,499353805,364673496,467223586,449496785,178345952,459815175,18011873,470207698,116570073,312413740,200929854,450539448,18079840,39721474,40325591,456309511,172296488,421548025,365159073,374217019,147077760,387580340,138053467}

    249166680

    Returns: 18936073

  26. {139104651,386592291,180841723,234027238,478479116,300748770,362528448,10191600,478073974,153655516,248717274,87513983,151995197}

    369406659

    Returns: 97705583

  27. {224772158,40820874,466288682,250395384,195692656,430739639,35578402,186814934,158450033,485308632,354718624,397313719,233703207,249228332,298904843,379510572,126542226,253675183,455224091,463437752,324960327,67196300,409186398,486628686,359313900,464616868,329105330,104000985,48078270,24727051,447134673,452940985,173005577,436833671,59805630,231433790,198356914,129275925,129859678,131657009}

    291148040

    Returns: 49734865

  28. {202778588,260230729,368612237,189377375,203319103,45418676,485638632,393577366,325388255,351916184,341789432,2225367,392152812,246364039,70645248,260946853,14227171,290940430,187986140,155696562,70808350,150765352,119367547,423884135,62434626,303452619,435741793,420799581,8277198,267638105,206928422,251698920,419629458,80811568,448130290}

    360318567

    Returns: 10502565

  29. {370030363,299625991,471912318,494097071,24453085,388852790,263770156,276842956,313337006,352481129,414534328,340238769,121982647,98232089,11829362,52677454,337912724,258940885,257291623,387246319,486878938,485596353,406605519}

    391867701

    Returns: 36282447

  30. {6,10,2,5,2,5,5,9,5,10,4,2}

    4

    Returns: 3

  31. {8,4,10,8,7,3,3,4,10,10,7,9,10,7,2}

    3

    Returns: 3

  32. {8,10,8,10,2,4,6,6,2,7,9,5,3,4,7,4,8,9,3}

    8

    Returns: 3

  33. {3,3,7,5,7,2,4,8,5,10,4,9,5,9,4,2,8,4}

    15

    Returns: 3

  34. {5,5,4,5,5,4,3,6,6,8,9,9,5}

    0

    Returns: 3

  35. {10,8,4,6,2,6,5,8,3,9,7,6,10,6,5,6,5}

    14

    Returns: 4

  36. {10,5,5,2,6,3,4,8,5,5}

    10

    Returns: 4

  37. {5,10,4,3,4,4,8,7,2,3,7,9,10,4}

    4

    Returns: 4

  38. {6,2,7,10,2,2,3,4,7,8,10,5}

    19

    Returns: 3

  39. {3,7,8,2,3,5,9,10,4,5,4,3,5,3,7,2}

    12

    Returns: 3

  40. {150421142,162364615,72758362,212587823,301878381,451868829,419074050,267428994,161862087,44749444,293029662,444733919,354441902,407043072,442865955,293877114,222393384,337756703,188134334,191465061,166093226,286040587,178342222,73429757,306115229,39263870,48811625,194610556,503522,29463368,373862487,276906089,365681222,68866761,90951059,332365344,472331027,56043135,148882766,415877458,282100099,143644527,273972203,85612165,128248131,491545273,165310340,71374736,183246581,465707283}

    0

    Returns: 503522

  41. {250757476,487592230,429226927,265955904,77010571,64849987,393826940,229448607,260035883,161724,462955484,79607454,422485554,71883965,458922557,87769405,354959286,200946241,352578182,426853272,426962826,55631258,183824532,249166680,369096882,364629999,263620532,324512826,247393767,233076917,288933670,75313813,366433555,2626617,18089890,499353805,364673496,467223586,449496785,178345952,459815175,18011873,470207698,116570073,312413740,200929854,450539448,18079840,39721474,40325591}

    0

    Returns: 161724

  42. {456309511,172296488,421548025,365159073,374217019,147077760,387580340,138053467,334941761,369406659,139104651,386592291,180841723,234027238,478479116,300748770,362528448,10191600,478073974,153655516,248717274,87513983,151995197,20256037,291148040,224772158,40820874,466288682,250395384,195692656,430739639,35578402,186814934,158450033,485308632,354718624,397313719,233703207,249228332,298904843,379510572,126542226,253675183,455224091,463437752,324960327,67196300,409186398,486628686,359313900}

    0

    Returns: 10191600

  43. {464616868,329105330,104000985,48078270,24727051,447134673,452940985,173005577,436833671,59805630,231433790,198356914,129275925,129859678,131657009,288343983,360318567,202778588,260230729,368612237,189377375,203319103,45418676,485638632,393577366,325388255,351916184,341789432,2225367,392152812,246364039,70645248,260946853,14227171,290940430,187986140,155696562,70808350,150765352,119367547,423884135,62434626,303452619,435741793,420799581,8277198,267638105,206928422,251698920,419629458}

    0

    Returns: 2225367

  44. {150126752,53706184,132515414,406609022,252475770,466417688,390188571,233331028,246781146,364782551,244552115,42485675,492650007,459782893,34260287,498868937,426617796,168572581,59754856,315078555,247601980,481359151,473367518,285436470,421227039,425308957,192539854,48585807,354914513,273647338,263369326,242668221,318364659,425130609,321276792,93848065,444377078,234171760,17537445,356093369,65226884,11665674,0,446754349,129707541,270681672,392983158,433791942,307590232,421892245}

    0

    Returns: 0

  45. {3728340,200899445,47688159,472381214,475490869,80343482,116583085,218551273,103767569,404224739,200869487,214588266,373162426,399764476,333817231,194407759,363194957,31658485,175603317,137972072,342690858,39789605,205306389,460571438,297486704,369455037,232165730,241218871,408001929,313551197,355757270,32727491,214391198,6310276,319470829,358811187,9847071,424059924,239326376,292507276,126745147,41079510,320364,147946233,320351,115028984,68858272,474537799,460551917,127376004}

    17

    Returns: 320366

  46. {499999997,500000000,499999995,500000000,499999995,499999996,499999993,499999995,499999993,499999994,499999997,499999998,499999993,499999993,499999993,499999996,499999993,499999996,499999996,500000000,499999993,499999993,499999995,499999994,500000000,499999995,499999997,499999993,500000000,500000000,499999998,499999995,499999998,499999995,499999997,499999999,499999995,499999995,499999998,499999996,499999997,499999994,500000000,499999999,499999999,499999999,500000000,499999993,499999997,499999997}

    33

    Returns: 499999995

  47. {483377682, 483382290, 498765432, 483377150, 483379338, 483374318, 498765432, 498765432, 483378026, 483381781, 483380812, 483388741, 483362966, 483372988, 483375302, 498765432, 483379637, 483364204, 483382169, 498765432, 498765432, 498765432, 483363010, 483363580, 498765432, 483365711, 483383171, 498765432, 498765432, 483359372, 498765432, 483363516, 483375743, 483378755, 498765432, 498765432, 498765432, 483378059, 483376210, 498765432, 498765432, 483376712, 483377199, 483378236, 498765432, 498765432, 498765432, 483367848, 483370042, 498765432 }

    500000000

    Returns: 499521289

  48. {1, 4, 6, 6, 6, 6 }

    10000

    Returns: 5

  49. {10, 10, 10, 10, 10, 10, 10, 10, 10, 10 }

    10

    Returns: 11

  50. {2, 3, 4, 5, 6 }

    4

    Returns: 4

  51. {500000000, 500000000 }

    500000000

    Returns: 750000000

  52. {3, 3, 3 }

    100000

    Returns: 4

  53. {500000000, 500000000, 500000000, 500000000, 500000000 }

    500000000

    Returns: 600000000

  54. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    500000000

    Returns: 510000000

  55. {6, 6, 6, 6, 6, 6 }

    6

    Returns: 7

  56. {100, 10, 1 }

    100

    Returns: 11

  57. {1, 1 }

    100

    Returns: 2

  58. {22222, 33333, 22222, 33333, 55555, 66666, 77777, 88888, 99999, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    500000000

    Returns: 37036

  59. {5, 0, 8, 5, 415, 0, 9 }

    51515

    Returns: 0

  60. {0, 0 }

    1

    Returns: 0

  61. {500000, 3442342, 123123123, 342334, 2342343, 4334344, 3434231, 34343434, 1, 1, 500000, 3442342, 123123123, 342334, 2342343, 4334344, 3434231, 34343434, 1, 1, 500000, 3442342, 123123123, 342334, 2342343, 4334344, 3434231, 34343434, 1, 1, 500000, 3442342, 123123123, 342334, 2342343, 4334344, 3434231, 34343434, 1, 1 }

    500000000

    Returns: 1

  62. {1, 1, 1, 1000000 }

    1000000

    Returns: 1

  63. {490000001, 490000002, 490000003, 490000007, 500000000 }

    500000000

    Returns: 592000002

  64. {59475, 68237, 56303, 87177, 92318, 90893, 65164, 61990, 67419, 65088, 91487, 99098, 63518, 94527, 56230, 88558, 81539, 82852, 53553, 96136, 51615, 61983, 93885, 92770, 92583, 91693, 86938, 66345, 88199, 92828, 81734, 65583, 79829, 69544, 93576, 95937, 96011, 86793, 85734, 54050, 57488, 58443, 89607, 65462, 95583, 67724, 89369, 72568, 80958, 54313 }

    1000000

    Returns: 62544

  65. {3, 3, 4 }

    10000000

    Returns: 5

  66. {40877, 18411599, 6314998, 26420500, 19111493, 15676828, 11443566, 29269926, 26881114, 24390608, 5687885, 28060565, 23211157, 16776519, 9931117, 489527, 2986015, 11906174, 4812519, 5419692, 32293827, 14560188, 3890294, 152541, 291124, 12344854, 17368737, 18659852, 19658846, 19835315, 5430659, 21660822, 14726687, 11503386, 1863393, 19852264, 25589999, 26220103, 16983895, 9864318, 28616891, 23739567, 31228034, 30242001, 17619981, 4650008, 15095577, 7687867, 28168241, 6847396 }

    500000000

    Returns: 193418

  67. {5 }

    5

    Returns: 10

  68. {500000000 }

    500000000

    Returns: 1000000000

  69. {18823, 127123, 1271, 1277, 51726, 5775, 1773, 1884, 1751, 3717, 4661, 38192, 128771, 1883199, 1773 }

    19889

    Returns: 1945

  70. {1000, 1000, 1000 }

    10000000

    Returns: 1500

  71. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 496000000, 496000000, 496000000, 496000000, 496000000, 496000000, 496000000, 496000000, 500000000, 500000000, 500000000, 499999999, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 496000000, 496000000, 496000000, 496000000, 496000000, 496000000, 496000000, 494543534, 500000000, 500000000, 500000000, 499999999 }

    500000000

    Returns: 509875989

  72. {500000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    15

    Returns: 0

  73. {500000000, 499999996, 499999999, 460000001 }

    494534686

    Returns: 613633670

  74. {4, 4, 4, 4 }

    1000

    Returns: 5

  75. {1, 1, 1, 7 }

    8

    Returns: 1

  76. {2, 2, 8 }

    10

    Returns: 4

  77. {1, 1, 1, 1, 1, 1 }

    500000

    Returns: 1

  78. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 500000000, 499999999, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 100000001, 100000000, 99999999, 99999998, 123456789, 87654321, 123, 234, 345, 456, 567, 678, 789, 11, 13, 100000000, 456345234, 45454, 35353, 987, 876, 765, 654, 543, 432, 321, 0 }

    499999999

    Returns: 0

  79. {2, 2, 2, 3, 3, 3, 15000, 10000 }

    1000

    Returns: 3

  80. {500000, 3442342, 123123123, 342334, 2342343, 4334344, 3434231, 34343434, 1, 1, 500000, 3442342, 123123123, 342334, 2342343, 4334344, 3434231, 34343434, 1, 1, 500000, 3442342, 123123123, 342334, 2342343, 4334344, 3434231, 34343434, 1, 1, 500000, 3442342, 123123123, 342334, 2342343, 4334344, 3434231, 34343434, 1, 1, 500000000 }

    500000000

    Returns: 1

  81. {0, 0, 0, 0, 0, 500000000 }

    500000000

    Returns: 0

  82. {0, 0 }

    10

    Returns: 0

  83. {4, 5 }

    1

    Returns: 5

  84. {1, 4, 6, 6, 6, 6 }

    1000000

    Returns: 5

  85. {1 }

    5

    Returns: 6

  86. {1, 2, 3, 4 }

    9999

    Returns: 3

  87. {10, 8, 6, 561, 21 }

    20

    Returns: 12

  88. {0, 0 }

    100000

    Returns: 0

  89. {500000000, 400000000, 30, 20, 25 }

    455445445

    Returns: 37

  90. {1, 1, 6, 7, 1, 1 }

    1000

    Returns: 1

  91. {3, 3, 3 }

    3

    Returns: 4

  92. {1, 2 }

    10000

    Returns: 3

  93. {1, 2, 3 }

    10000

    Returns: 3

  94. {500000000, 18, 9, 7, 12, 15, 3, 1, 2, 1, 0 }

    500000000

    Returns: 1

  95. {0 }

    1

    Returns: 1

  96. {2257151, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 39485105, 33929299 }

    46143145

    Returns: 36186450

  97. {499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999 }

    499999996

    Returns: 509999998

  98. {500000000, 500000000, 500000000 }

    500000000

    Returns: 666666666

  99. {2, 3, 4, 5, 6 }

    5

    Returns: 4

  100. {2, 2, 2 }

    100

    Returns: 3

  101. {1, 1, 4 }

    8

    Returns: 2

  102. {1, 2, 3 }

    4

    Returns: 3

  103. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    499999999

    Returns: 509999999

  104. {1, 1, 1, 2 }

    10

    Returns: 1

  105. {3, 1, 1 }

    4

    Returns: 2

  106. {1000, 1000, 1000, 1000 }

    1000000

    Returns: 1333

  107. {5, 3, 2, 1 }

    10000000

    Returns: 3

  108. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 490000000, 490000000, 490000000, 490000000, 490000000, 490000000, 490000000, 490000000, 490000000, 490000000, 480000000, 480000000, 480000000, 480000000, 480000000, 480000000, 480000000, 480000000, 480000000, 480000000, 470000000, 470000000, 470000000, 470000000, 470000000, 470000000, 470000000, 470000000, 470000000, 470000000, 460000000, 460000000, 460000000, 460000000, 460000000, 460000000, 460000000, 460000000, 460000000, 460000000 }

    475000000

    Returns: 485833333

  109. {3, 4, 5, 6 }

    10000

    Returns: 6

  110. {100, 101, 100000 }

    300

    Returns: 201

  111. {1, 2 }

    10

    Returns: 3

  112. {4, 4, 4 }

    100000

    Returns: 6

  113. {200000000, 200000001, 200000002, 200000003 }

    200000000

    Returns: 250000001

  114. {33, 23, 14 }

    41

    Returns: 35

  115. {1, 500000000 }

    500000000

    Returns: 500000000

  116. {5, 6, 7 }

    100

    Returns: 9

  117. {2, 2 }

    100

    Returns: 4

  118. {40, 40, 40 }

    3

    Returns: 41

  119. {3, 3, 3, 3, 3 }

    5

    Returns: 3

  120. {500000000, 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, 1, 1 }

    500000000

    Returns: 1

  121. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    500000000

    Returns: 571428571

  122. {3741, 2358, 21789, 537, 34812, 2751 }

    2718

    Returns: 2788

  123. {200, 300, 400 }

    111111

    Returns: 450

  124. {10000, 9999, 9998, 9997, 9997, 9995, 9996, 9995, 9993, 9991, 9989, 9980, 9979, 9980, 9500, 8990, 10000, 10000 }

    9000

    Returns: 10409

  125. {10, 8, 6, 561, 21, 50000000, 10035435 }

    56146540

    Returns: 12

  126. {4, 4, 4, 4 }

    50000000

    Returns: 5

  127. {999999, 10001, 999, 765, 100001 }

    50

    Returns: 815

  128. {7, 7, 7, 7, 7 }

    7

    Returns: 8

  129. {10, 15 }

    300

    Returns: 25

  130. {10, 10, 10 }

    1000

    Returns: 15

  131. {8, 8 }

    8

    Returns: 12

  132. {1, 0, 0 }

    2

    Returns: 0

  133. {5, 5, 5, 5, 5 }

    5000000

    Returns: 6

  134. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 411172541, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 491876541, 500000000, 500000000 }

    500000000

    Returns: 508060981

  135. {10, 10, 10, 10, 10, 10 }

    1000

    Returns: 12

  136. {10000000, 10000001, 20000003 }

    50000000

    Returns: 20000001

  137. {50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 0 }

    500000000

    Returns: 50000000

  138. {4, 4, 4, 4 }

    4

    Returns: 5

  139. {0, 250000000, 500000000 }

    500000000

    Returns: 250000000

  140. {2, 2 }

    2

    Returns: 3

  141. {3, 3, 3 }

    20

    Returns: 4

  142. {0, 0 }

    1000

    Returns: 0

  143. {5, 5, 5 }

    10

    Returns: 7

  144. {7 }

    20

    Returns: 27

  145. {3, 1, 6, 7 }

    500000000

    Returns: 4

  146. {3, 3, 3, 3 }

    4

    Returns: 4

  147. {10, 10, 10, 10 }

    99999

    Returns: 13

  148. {10, 10, 10 }

    500000000

    Returns: 15

  149. {4, 4, 4, 10, 10 }

    20

    Returns: 6

  150. {1, 1 }

    4

    Returns: 2

  151. {50, 50, 50, 50, 50 }

    400000000

    Returns: 62

  152. {3, 3, 4, 5 }

    10

    Returns: 5

  153. {36629216, 37215528, 37379060, 40873980, 49646416, 69909134, 80835680, 82426872 }

    2000000

    Returns: 37741268

  154. {200000000, 200000001, 200000002, 200000003, 200000004 }

    200000000

    Returns: 240000002

  155. {50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000, 50000000 }

    500000000

    Returns: 51020408

  156. {1000, 1000, 1000, 1000, 1000 }

    1000

    Returns: 1200

  157. {100000000, 100000000 }

    100000000

    Returns: 150000000

  158. {2, 3, 4, 5, 6 }

    999

    Returns: 4

  159. {1, 2 }

    100

    Returns: 3

  160. {1, 2, 3, 5, 500000000 }

    500000000

    Returns: 3

  161. {10, 11, 12, 13, 14, 15, 16 }

    10

    Returns: 14

  162. {1, 1, 1, 2, 2 }

    5

    Returns: 1

  163. {250000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    500000000

    Returns: 506410256

  164. {7, 7, 7, 8, 8, 9, 9, 10, 16 }

    1000

    Returns: 9

  165. {5, 3, 2, 4, 5, 76, 84, 3 }

    0

    Returns: 2

  166. {6, 6, 6, 100 }

    500000000

    Returns: 9

  167. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    500000000

    Returns: 522727272

  168. {10, 10, 10 }

    15

    Returns: 15

  169. {100, 101, 100, 999, 9999, 4258, 44457, 77787, 787, 454, 787878 }

    19959782

    Returns: 150

  170. {1, 1, 1, 1, 15 }

    60

    Returns: 1

  171. {2, 2 }

    24

    Returns: 4

  172. {3, 3, 4 }

    5

    Returns: 5

  173. {0 }

    5

    Returns: 5

  174. {1, 1, 20 }

    100

    Returns: 2

  175. {499999999, 499999999, 499999999, 499999999, 499999999 }

    499999999

    Returns: 599999998

  176. {1, 1, 3 }

    4

    Returns: 2

  177. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 0 }

    500000000

    Returns: 500000000

  178. {500000000, 400000000, 200000000, 100000000, 300000000 }

    500000000

    Returns: 300000000

  179. {450000000, 450000100, 450000200, 450000300, 450001000, 450000900, 450000800, 450000700, 450000600, 450000500, 450000400, 450000350, 450002000 }

    500000

    Returns: 450039065

  180. {499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 499999999, 299999999, 399999999 }

    499999999

    Returns: 519999998

  181. {1, 2 }

    500000000

    Returns: 3

  182. {0 }

    0

    Returns: 0

  183. {1, 2 }

    3

    Returns: 3

  184. {9, 9, 9, 9 }

    12

    Returns: 12

  185. {0, 0, 10 }

    4

    Returns: 0

  186. {100, 100, 100, 100 }

    40

    Returns: 110

  187. {1, 1, 10 }

    3

    Returns: 2

  188. {3, 4, 5 }

    6

    Returns: 6

  189. {1, 1, 2, 3 }

    1000000

    Returns: 2

  190. {2, 3, 3 }

    100000

    Returns: 4

  191. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    123456

    Returns: 500002469

  192. {1, 1, 1, 4 }

    9

    Returns: 1

  193. {5, 5 }

    10

    Returns: 10

  194. {100, 100 }

    5

    Returns: 102

  195. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    500000000

    Returns: 520833333

  196. {5000000, 5000000, 4000000, 6000000, 7000000, 4567868, 453212, 3578694, 97897898, 45645678, 14725725 }

    499999999

    Returns: 4015953

  197. {2, 3, 5 }

    4

    Returns: 4

  198. {101, 102, 103 }

    3

    Returns: 103

  199. {400000000, 400000003, 500000000, 4123455, 43343334, 43343334, 43341334, 43143334, 13343334, 23343334, 41343334, 13343334, 43343334, 443433478, 500000000, 89898898, 12343, 35355445, 766776, 35155445, 35055445, 37355445, 343434, 899878 }

    500000000

    Returns: 355777

  200. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    500000000

    Returns: 512195121

  201. {5, 6, 7, 8, 9, 10 }

    3

    Returns: 7

  202. {1, 5, 5, 100, 100 }

    1000000

    Returns: 5

  203. {4, 5, 6 }

    6

    Returns: 7

  204. {2, 2, 2, 2 }

    1000

    Returns: 2

  205. {1, 1 }

    100000

    Returns: 2

  206. {50, 51 }

    1

    Returns: 51

  207. {3, 3, 3 }

    10000

    Returns: 4

  208. {10, 10, 10 }

    20

    Returns: 15

  209. {2, 3, 4 }

    5

    Returns: 4

  210. {0 }

    13

    Returns: 13

  211. {1, 1, 1, 1, 2 }

    1000

    Returns: 1

  212. {9, 10, 11, 12 }

    200

    Returns: 14

  213. {4, 5, 6 }

    100

    Returns: 7

  214. {1, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    500000000

    Returns: 500000000

  215. {3, 4 }

    10

    Returns: 7

  216. {1, 1 }

    1000000

    Returns: 2

  217. {2, 4, 4, 4 }

    5000

    Returns: 4

  218. {300000000, 300000001, 300000002, 300000003, 300000004, 300000005, 300000006, 300000007, 300000008, 300000009, 400000000, 400000000, 400000000, 400000000, 400000000, 400000000, 400000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000, 300000000 }

    450000000

    Returns: 310000001

  219. {234, 4532, 111, 17, 909, 645, 34235, 3421, 9, 22, 13454 }

    4503

    Returns: 24

  220. {10, 10, 10 }

    10

    Returns: 13

  221. {50, 50, 50, 50, 50, 60 }

    400000000

    Returns: 62

  222. {1, 0, 0 }

    1000

    Returns: 0

  223. {0, 1, 2 }

    0

    Returns: 0

  224. {2, 2 }

    1000

    Returns: 4

  225. {123456789, 321654987, 333444555, 111222333, 222333444, 444555666, 444333222, 333222111, 111999888 }

    344355366

    Returns: 173339505

  226. {481964, 375105, 805739, 494426, 302932, 149913, 361663, 64287, 984870, 909404, 26350, 750888, 315721, 670733, 901153, 793373, 94615, 300103, 552318, 55672, 737067, 498846, 860779, 931250, 290060, 787433, 91462, 831000, 560442, 120440, 548133, 682104, 736278, 170808, 27905, 165389, 213774, 136093, 929046, 806588, 23102, 474996, 147068, 734272, 804011, 282090, 562751, 417517, 294102, 445616 }

    324324543

    Returns: 38678

  227. {0, 0, 1 }

    2

    Returns: 0

  228. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    5000

    Returns: 500000833

  229. {1, 1, 1 }

    1000

    Returns: 1

  230. {1, 1, 1, 1, 1, 1, 1, 1 }

    500000000

    Returns: 1

  231. {2 }

    5

    Returns: 7

  232. {100, 101, 102, 103, 10000 }

    700

    Returns: 135

  233. {100, 100, 100, 100, 100, 100, 100, 100, 100, 100 }

    10000

    Returns: 111

  234. {2, 2, 4 }

    5000

    Returns: 4

  235. {2, 2 }

    10000

    Returns: 4

  236. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    500000000

    Returns: 510869565

  237. {3, 3, 7 }

    3

    Returns: 4

  238. {3, 3, 3, 4 }

    3

    Returns: 4

  239. {1, 1, 3, 4 }

    4

    Returns: 2

  240. {4, 4 }

    10

    Returns: 8

  241. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    500000000

    Returns: 545454545

  242. {100, 100, 2, 3, 4, 9, 111, 3, 999 }

    10000

    Returns: 4

  243. {1, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    500000000

    Returns: 500000000

  244. {383282690, 44683266, 185210335, 146366464, 495417444, 408214433, 460439854, 362414541, 139280080, 361045535, 191805158, 431673452, 265028925, 430096963, 413205721, 348357544, 342142447, 14574873, 93549435, 286274760, 401686631, 263247611, 222254232, 142314231, 350905186, 214252401, 356214249, 87940568, 98274149, 89149868, 420762639, 269163709, 386554827, 13529006, 86973200, 279117279, 17245894, 204545747, 160832692, 355627440, 345232484, 193647446, 422992375, 340967896, 215862898, 147514360, 484588979, 36508969, 132133122, 324901874 }

    16926604

    Returns: 20758792

  245. {200000000, 210000000, 220000000, 230000000, 240000000, 200000000, 200000000, 200000000, 200000000, 200000000, 200000000, 200000000, 200000000, 200000000, 200200000, 200000000, 200000000, 200000000, 380006000, 400000000, 490000111 }

    432555666

    Returns: 215014285

  246. {1, 102 }

    50000

    Returns: 103

  247. {2, 2, 2 }

    10000

    Returns: 3

  248. {10, 10, 15 }

    12

    Returns: 15

  249. {10, 10, 10, 20 }

    6

    Returns: 12

  250. {500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000, 500000000 }

    500000

    Returns: 500010000

  251. {1, 1, 1, 4 }

    10

    Returns: 1

  252. {3, 3 }

    3

    Returns: 4

  253. {3, 4, 5 }

    10

    Returns: 6

  254. {3, 3 }

    5

    Returns: 5

  255. {100000000, 100000000, 100000000, 100000000, 100000000 }

    100000000

    Returns: 120000000

  256. {0, 0, 0, 9, 9, 9 }

    6

    Returns: 0

  257. {5, 8, 9 }

    100000000

    Returns: 11

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