Statistics

Problem Statement for "RedAndBlueShades"

Problem Statement

We have several bags. Each bag contains one or more marbles. Each marble is either some shade of red, or some shade of blue. Globally, all marbles are mutually distinct.

We also have an unlimited supply of new empty bags. All bags, both original and new ones, look exactly the same.


Your collection of bags is described by two equally-long int[]s R and B. For each valid index i, one of the bags in your collection contains R[i] marbles in shades of red and B[i] marbles in shades of blue.


Let a step be the following operation: "For each bag that contains more than one marble, take all the marbles it contains and divide them into two new bags so that both new bags are non-empty."

Let the process be any sequence of steps that begins with our current collection of bags and ends with a collection of bags that contain one marble each.

The blue marbles can be handled arbitrarily, but for red marbles there is an extra restriction: whenever you are performing a split and you want to put a single red marble into a bag (that will become its final bag), you must put more than one marble into the other bag.

The process is called valid if we always obey the rule for red marbles.


Count all valid processes, and return that count modulo 10^9 + 7.

Definition

Class:
RedAndBlueShades
Method:
count
Parameters:
long[], long[]
Returns:
int
Method signature:
int count(long[] R, long[] B)
(be sure your method is public)

Constraints

  • R will contain between 1 and 10 elements, inclusive.
  • B will contain the same number of elements as R.
  • All elements of R and B will be non-negative.
  • For each i, R[i] + B[i] will not exceed 10^12.
  • No bag will be empty: for each i, R[i] + B[i] will be positive.

Examples

  1. {0}

    {4}

    Returns: 15

    We start with a single bag containing four distinct blue marbles. Let's label the marbles 0 to 3. All possible processes are shown below. (One per row, arrows represent steps. Note that some processes only have two steps while others have three.) {{0,1,2,3}} -> {{0,1}, {2,3}} -> {{0}, {1}, {2}, {3}} {{0,1,2,3}} -> {{0,1,2}, {3}} -> {{0,1}, {2}, {3}} -> {{0}, {1}, {2}, {3}} {{0,1,2,3}} -> {{0,1,2}, {3}} -> {{0}, {1,2}, {3}} -> {{0}, {1}, {2}, {3}} {{0,1,2,3}} -> {{0}, {1,2,3}} -> {{0}, {1,2}, {3}} -> {{0}, {1}, {2}, {3}} {{0,1,2,3}} -> {{0}, {1,2,3}} -> {{0}, {1}, {2,3}} -> {{0}, {1}, {2}, {3}} {{0,1,2,3}} -> {{0}, {1,2,3}} -> {{0}, {1,3}, {2}} -> {{0}, {1}, {2}, {3}} {{0,1,2,3}} -> {{0,1,2}, {3}} -> {{0,2}, {1}, {3}} -> {{0}, {1}, {2}, {3}} {{0,1,2,3}} -> {{0,1,3}, {2}} -> {{0,1}, {2}, {3}} -> {{0}, {1}, {2}, {3}} {{0,1,2,3}} -> {{0,1,3}, {2}} -> {{0}, {1,3}, {2}} -> {{0}, {1}, {2}, {3}} {{0,1,2,3}} -> {{0,1,3}, {2}} -> {{0,3}, {1}, {2}} -> {{0}, {1}, {2}, {3}} {{0,1,2,3}} -> {{0,2}, {1,3}} -> {{0}, {1}, {2}, {3}} {{0,1,2,3}} -> {{0,2,3}, {1}} -> {{0}, {1}, {2,3}} -> {{0}, {1}, {2}, {3}} {{0,1,2,3}} -> {{0,2,3}, {1}} -> {{0,2}, {1}, {3}} -> {{0}, {1}, {2}, {3}} {{0,1,2,3}} -> {{0,2,3}, {1}} -> {{0,3}, {1}, {2}} -> {{0}, {1}, {2}, {3}} {{0,1,2,3}} -> {{0,3}, {1,2}} -> {{0}, {1}, {2}, {3}}

  2. {17}

    {0}

    Returns: 0

    Regardless of how you make the individual steps, you will eventually encounter a situation where you want to split a bag with exactly two red marbles. At that moment you are forced to violate the rule for red marbles.

  3. {1, 1, 1, 0, 0, 1, 0, 1, 0, 0}

    {0, 0, 0, 1, 1, 0, 1, 0, 1, 1}

    Returns: 1

    Each bag already contains exactly one marble. The only valid process is the trivial process that consists of zero steps.

  4. {3, 4, 3, 4}

    {4, 3, 5, 4}

    Returns: 959845692

    Make sure to compute and return the answer modulo 10^9 + 7.

  5. {1}

    {3}

    Returns: 6

    One more annotated example: all valid processes for a bag with a single red marble (R) and three blue marbles (B0,B1,B2). {{R,B0,B1,B2}} -> {{B0,B1,B2}, {R}} -> {{B0}, {B1,B2}, {R}} -> {{B0}, {B1}, {B2}, {R}} {{R,B0,B1,B2}} -> {{B0,B1,B2}, {R}} -> {{B0,B2}, {B1}, {R}} -> {{B0}, {B1}, {B2}, {R}} {{R,B0,B1,B2}} -> {{B0,B1,B2}, {R}} -> {{B0,B1}, {B2}, {R}} -> {{B0}, {B1}, {B2}, {R}} {{R,B0,B1,B2}} -> {{B0}, {R,B1,B2}} -> {{B0}, {B1,B2}, {R}} -> {{B0}, {B1}, {B2}, {R}} {{R,B0,B1,B2}} -> {{B1}, {R,B0,B2}} -> {{B0,B2}, {B1}, {R}} -> {{B0}, {B1}, {B2}, {R}} {{R,B0,B1,B2}} -> {{B2}, {R,B0,B1}} -> {{B0,B1}, {B2}, {R}} -> {{B0}, {B1}, {B2}, {R}}

  6. {10999999, 10999999, 10999999, 10999999, 10999999, 10999999, 10999999, 10999999, 10999999, 10999999}

    {100999999, 100999999, 100999999, 100999999, 100999999, 100999999, 100999999, 100999999, 100999999, 100999999}

    Returns: 568969561

  7. {100999999, 100999999, 100999999, 100999999, 100999999, 100999999, 100999999, 100999999, 100999999, 100999999}

    {100999999, 100999999, 100999999, 100999999, 100999999, 100999999, 100999999, 100999999, 100999999, 100999999}

    Returns: 380819905

  8. {205504635}

    {478808774}

    Returns: 737686359

  9. {1, 8}

    {6, 7}

    Returns: 55038827

  10. {5, 8, 6}

    {4, 6, 9}

    Returns: 469444470

  11. {6}

    {10}

    Returns: 789836458

  12. {1}

    {0}

    Returns: 1

  13. {7, 0}

    {8, 5}

    Returns: 65612981

  14. {6, 3, 8}

    {3, 8, 5}

    Returns: 158423742

  15. {3, 8}

    {0, 5}

    Returns: 0

  16. {5, 5, 9}

    {9, 8, 3}

    Returns: 131111308

  17. {0}

    {2}

    Returns: 1

  18. {1, 9}

    {5, 6}

    Returns: 355759147

  19. {8, 1, 3}

    {4, 10, 5}

    Returns: 256492380

  20. {7}

    {1}

    Returns: 0

  21. {9, 10}

    {5, 4}

    Returns: 535674467

  22. {8}

    {4}

    Returns: 27216000

  23. {8, 0}

    {9, 7}

    Returns: 58283089

  24. {9, 4}

    {6, 8}

    Returns: 143919798

  25. {9}

    {1}

    Returns: 0

  26. {3, 7, 9}

    {6, 4, 8}

    Returns: 534852699

  27. {7}

    {0}

    Returns: 0

  28. {8}

    {10}

    Returns: 560748597

  29. {1}

    {4}

    Returns: 45

  30. {9, 7, 5}

    {8, 6, 0}

    Returns: 0

  31. {4, 9, 10}

    {10, 8, 7}

    Returns: 401009727

  32. {10, 0, 3}

    {5, 9, 3}

    Returns: 442278079

  33. {6, 2}

    {2, 7}

    Returns: 314344800

  34. {2}

    {1}

    Returns: 0

  35. {9}

    {5}

    Returns: 382527944

  36. {6, 4, 0}

    {1, 7, 10}

    Returns: 0

  37. {6}

    {1}

    Returns: 0

  38. {0, 0}

    {4, 2}

    Returns: 15

  39. {8}

    {7}

    Returns: 415673027

  40. {7}

    {8}

    Returns: 733958224

  41. {9, 0}

    {9, 1}

    Returns: 499175812

  42. {2}

    {8}

    Returns: 7567560

  43. {10, 9}

    {0, 3}

    Returns: 0

  44. {0, 1, 1}

    {6, 0, 4}

    Returns: 42525

  45. {8}

    {4}

    Returns: 27216000

  46. {9}

    {8}

    Returns: 131225962

  47. {8}

    {9}

    Returns: 281198490

  48. {9, 1}

    {9, 9}

    Returns: 745891262

  49. {298780335, 7690356, 224221883, 162571111, 525333703, 149950278, 68165869, 121238248, 350551292}

    {34603937, 24170072, 109873291, 108628589, 40300608, 245891540, 27844, 2230418, 72363936}

    Returns: 447448603

  50. {19196099, 434690389, 560627570, 71072587, 308839297, 756726466, 269721006, 101327947, 94540023}

    {432603813, 15969736, 22443729, 374318615, 265207308, 42406601, 128314833, 10608313, 84327621}

    Returns: 821364547

  51. {124167797, 19720713, 90051561, 247244343, 292551939, 25537871, 203243637, 729714784, 21950601}

    {27529323, 2269731, 7687326, 123053975, 2322863, 355533468, 199132584, 77579236, 143136013}

    Returns: 166093331

  52. {518276962, 36757419, 117075129, 559272524, 633503745, 512516892, 388654383, 334682124, 413384333}

    {31981389, 187620480, 329309891, 192379319, 63922441, 65282730, 94056605, 143218112, 14550078}

    Returns: 451877365

  53. {219977310, 679160796, 13781561, 327488403, 178646847, 386678572, 116822057, 100051728, 668324192, 457550043}

    {371111443, 53603960, 42203659, 111344048, 128152000, 96029654, 398516180, 388167473, 124772560, 170643562}

    Returns: 594580913

  54. {23473419, 60640904, 420753700, 287670031, 113070839, 112317342, 456901483, 321600643, 416452305}

    {15238364, 282585962, 286611251, 196507671, 80009871, 99386669, 21195006, 194244947, 30813005}

    Returns: 901891501

  55. {29405005, 155769482, 330373, 14184897, 491132366, 470167904, 276727007, 55033197, 66490532}

    {155728288, 5478770, 257371733, 7684212, 219456691, 44208933, 191307038, 130302898, 129466909}

    Returns: 358059960

  56. {180740965, 228705322, 135118488, 551082069, 168035058, 24768466, 653790074, 407292477}

    {136772993, 152756137, 58341228, 30619214, 57233894, 285466839, 166213138, 157705584}

    Returns: 386984247

  57. {495881981, 599484617, 183215351, 404816052, 45952094, 164547096, 194843137, 83679517, 220664316, 15060559}

    {68438466, 31497067, 4760799, 174420919, 414300500, 15240566, 401390653, 293103842, 150025710, 24827275}

    Returns: 62699024

  58. {160507800, 2396703, 149346959, 78153605, 417806775, 403040, 398281627, 338108473, 392250892}

    {14187408, 212418880, 260573077, 359950564, 91847248, 203565, 68933657, 75288497, 4234959}

    Returns: 909645108

  59. {430015013, 11547663, 451283482, 295549387, 82850912, 178541466, 255443424, 320153185}

    {59466471, 49044672, 198217285, 73390455, 14550234, 4590921, 139943700, 75742567}

    Returns: 551055202

  60. {281598138, 351539983, 402079442, 211144144, 213200474, 80090326, 130894463, 348932673}

    {71535153, 95692135, 31199208, 384803383, 63258011, 415092280, 5695175, 4344172}

    Returns: 324816994

  61. {33889451, 424667598, 47936701, 13238791, 87319693, 240774617, 226325723, 276680942, 329181419, 122125671}

    {39342469, 48296244, 25804673, 9343439, 291725597, 202568346, 163753846, 134281347, 218341806, 207407929}

    Returns: 807351067

  62. {19253771, 190339681, 373430602, 108546280, 509022207, 4941792, 429046081, 252599354, 595262024, 57292139}

    {23899963, 291181309, 75424551, 75280001, 73314381, 1329297, 254099200, 200683408, 38084229, 172197387}

    Returns: 806903342

  63. {21082245, 113697937, 226714736, 196738984, 19020632, 180549570, 177607406, 12440555, 105705854}

    {23975485, 259840809, 14946610, 366265700, 33424220, 186202580, 297089398, 35244332, 14765972}

    Returns: 864185450

  64. {129087309, 158309743, 235734230, 372498812, 96744363, 337321499, 4803151, 150078554, 88639392}

    {844389, 143467649, 177011170, 178333971, 364284326, 175701143, 52313621, 33313335, 28411117}

    Returns: 981137855

  65. {342876693, 768153274, 460599972, 378121270, 559767407, 456876900, 471503640, 363027981}

    {276159536, 28638403, 125857247, 82713940, 148268109, 50455513, 106692149, 52583631}

    Returns: 360923618

  66. {526842172, 6536874, 26345242, 460126676, 108567928, 415189113, 133179045, 44917977, 396628056}

    {127298603, 8905244, 162080436, 91881074, 429567221, 28142103, 246299980, 29238129, 36381962}

    Returns: 903588492

  67. {100649535, 873194536, 438917892, 398055588, 556148090, 371922578, 128335516, 246358736}

    {128831560, 54055385, 139644029, 52659352, 212882156, 69046069, 213082361, 371964051}

    Returns: 697540186

  68. {28325499, 529972178, 76239804, 175900271, 310391575, 6303157, 649218198, 23737683}

    {322644107, 24881844, 136477343, 274648714, 260397073, 35820395, 76209269, 148494825}

    Returns: 136377142

  69. {6766887, 185041599, 206399912, 230917733, 199009861, 54330633, 330817444, 20240645, 321677090, 59482964}

    {328072713, 45015762, 381746785, 182778852, 98801829, 44565948, 74786880, 8422370, 162698593, 196697826}

    Returns: 839149274

  70. {449159156, 267243428, 24371224, 606607706, 740287894, 526985908, 72631320, 31393423, 25771035}

    {228316794, 52942944, 125695677, 85420170, 17337953, 226074887, 87017036, 202020531, 455630648}

    Returns: 383982622

  71. {112019553, 279281104, 46325395, 670691068, 673872987, 236873166, 898059514, 8785214, 143240245}

    {46393096, 57303570, 24465858, 52579095, 138788196, 63564228, 15891648, 31996061, 182407671}

    Returns: 149273729

  72. {54955861, 113306169, 425909270, 79648458, 957867, 606036483, 12738098, 114352867}

    {59635621, 65448001, 40792602, 66182348, 2709474, 21527307, 430946145, 77635178}

    Returns: 132707497

  73. {252871754, 230058198, 214997572, 41161877, 694139976, 445302559, 288621817, 4016761, 2759091, 26085799}

    {73639842, 376989927, 70969672, 468672263, 14249290, 92210335, 30413910, 183064339, 57293908, 153908715}

    Returns: 844823213

  74. {220906307, 562896777, 657037158, 146439, 595556493, 52890094, 409671188, 102525831, 37212615, 682705091}

    {6946512, 159428276, 135579020, 1731065, 170303942, 289311286, 1025422, 197865394, 29590281, 21097687}

    Returns: 671917315

  75. {373515540, 4379984, 322894077, 334136497, 40950388, 474324241, 218381898, 773450369, 48281716}

    {87161696, 18109026, 1784210, 216426047, 7458988, 255041905, 139600813, 4397746, 154430273}

    Returns: 947380132

  76. {451425244, 52733647, 405221552, 94715296, 15994814, 19297544, 619324219, 205501001, 59808423}

    {232204392, 174154224, 177658185, 155295557, 150751107, 6714293, 53346647, 333223877, 37732022}

    Returns: 440671144

  77. {3547879, 223479761, 454231929, 136988490, 100854230, 494006315, 79222413, 5317904}

    {2315037, 117844232, 152498929, 241985000, 32245035, 42311538, 101392853, 37650929}

    Returns: 218220302

  78. {218273706, 631112252, 18925913, 18824810, 32920873, 136669034, 313656809, 449164981, 524059221, 623784894}

    {20503449, 76892102, 59399971, 477915007, 57077277, 210033745, 171813326, 81406255, 31835480, 16923095}

    Returns: 59903527

  79. {839551594, 581930457, 884453279, 777589859, 248279256, 162686522, 662212723, 963663275, 526189448}

    {41458568, 199151801, 46579900, 103707099, 335648805, 376527481, 138029056, 671095, 230552768}

    Returns: 613267503

  80. {332016440, 809428128, 650222602, 13736714, 868217808, 525742634, 438127919, 402588821, 324151370, 423562100}

    {324594096, 72781765, 155068157, 455444885, 44610129, 219834538, 280062851, 271756311, 325218391, 258841478}

    Returns: 464772611

  81. {669734590, 288540651, 501831491, 108815604, 115582222, 36450493, 685588141, 712797109, 613878494, 1176794}

    {117518880, 341052149, 208589737, 421924439, 436467735, 471557805, 131886541, 116431917, 188542313, 459309662}

    Returns: 925396246

  82. {171791451, 922606452, 855656830, 516391627, 347333594, 285257142, 355156688, 705675087, 220653916, 189624752}

    {387675742, 30357652, 24840857, 219474373, 324463474, 317271201, 289611929, 124592977, 347158175, 400082445}

    Returns: 738772800

  83. {713258932, 494629645, 822514784, 366068895, 566868632, 119742495, 190822315, 244278498, 907283297}

    {112305740, 219173600, 85415066, 302382944, 177039544, 414351548, 364419078, 365751535, 32590366}

    Returns: 28642511

  84. {849986754, 581779980, 849113146, 267547179, 392440295, 809727134, 526358251, 787348666, 182842244, 432322630}

    {67880093, 202004610, 39264230, 358966246, 256517957, 70663425, 198359401, 97180579, 407292228, 246811059}

    Returns: 489030585

  85. {350884231, 579282471, 277949393, 148720048, 882190772, 802872130, 717226780, 293876822, 418215816}

    {306025842, 197172384, 316034915, 382031259, 53802299, 83148250, 130277169, 317037434, 280974343}

    Returns: 848381851

  86. {593674310, 128444743, 399695759, 572360428, 312392336, 653481056, 750581442, 344474778, 41154509}

    {170313320, 409782730, 275374507, 207400769, 308902365, 140099684, 120139340, 321423957, 467652682}

    Returns: 103213314

  87. {478939336, 809825375, 157041994, 196573588, 368344619, 101654213, 223339634, 821755213, 658397254}

    {230409860, 66911347, 379144067, 391443145, 283305038, 417560051, 358098096, 41663553, 138957661}

    Returns: 251216131

  88. {733317428, 531718764, 409898425, 24998314, 823531873, 160956422, 450237810, 236574870, 806490794}

    {96652676, 217181533, 250247811, 481057475, 82150142, 409305814, 232023305, 351912171, 74540774}

    Returns: 142633752

  89. {460023130}

    {92510152}

    Returns: 318361647

  90. {11982556}

    {588454245}

    Returns: 0

  91. {338618884}

    {331842645}

    Returns: 545769298

  92. {97788329}

    {127501683}

    Returns: 677050307

  93. {113740333}

    {488128802}

    Returns: 161381815

  94. {731569604}

    {93030635}

    Returns: 496529871

  95. {63742419}

    {235075023}

    Returns: 3329884

  96. {406938846}

    {331150913}

    Returns: 827413423

  97. {163038977}

    {63742693}

    Returns: 920641301

  98. {270618263}

    {490941911}

    Returns: 689090882

  99. {137187164}

    {550743712}

    Returns: 0

  100. {342001492}

    {304290805}

    Returns: 568166610

  101. {66786240}

    {554339969}

    Returns: 0

  102. {613720295}

    {225195979}

    Returns: 431573838

  103. {256920389}

    {203371246}

    Returns: 465693066

  104. {1094279840}

    {31547554}

    Returns: 0

  105. {213199019}

    {316428352}

    Returns: 288717891

  106. {541555155}

    {361553583}

    Returns: 532800726

  107. {400184362}

    {351951338}

    Returns: 587056824

  108. {709487332}

    {168785931}

    Returns: 34852167

  109. {75565005}

    {81103305}

    Returns: 530870477

  110. {241622101}

    {498449467}

    Returns: 102549786

  111. {1057243699}

    {100871023}

    Returns: 0

  112. {303088382}

    {358398435}

    Returns: 541654603

  113. {40521475}

    {459009036}

    Returns: 597581281

  114. {173710797}

    {410764214}

    Returns: 912037312

  115. {172951437}

    {313460938}

    Returns: 745847881

  116. {389412330}

    {195834966}

    Returns: 40893905

  117. {38944609}

    {331775805}

    Returns: 934783074

  118. {13236002}

    {508593434}

    Returns: 0

  119. {610717618}

    {9910859}

    Returns: 228154196

  120. {55807449}

    {593660090}

    Returns: 0

  121. {243875083}

    {487591577}

    Returns: 395439755

  122. {279452318}

    {88814261}

    Returns: 533839279

  123. {100498406}

    {475924931}

    Returns: 867271475

  124. {862699622}

    {49291936}

    Returns: 837140425

  125. {140625491}

    {571418087}

    Returns: 0

  126. {3556189}

    {599028848}

    Returns: 0

  127. {130322929}

    {580321032}

    Returns: 0

  128. {846112932}

    {170221973}

    Returns: 0

  129. {480929297, 588010765}

    {197533276, 711839980099}

    Returns: 0

  130. {303837050218, 244640136471, 148065548}

    {281147610389, 68245552, 65642875}

    Returns: 0

  131. {588010765, 101020612, 387453591, 197845379, 307193054}

    {711839980099, 286870342640, 154611118115, 14977198, 11266341}

    Returns: 0

  132. {482794486, 209762398, 149741382337, 275785662}

    {74033144, 831474183860, 65309119, 814639631278}

    Returns: 0

  133. {202396397, 522820014, 265601509, 192209615, 338394543}

    {472555640755, 490436713950, 555774917247, 161870362, 163739767}

    Returns: 0

  134. {101471983263, 328610375, 606349786693, 671266600659, 952019407790}

    {250408486470, 323135905582, 81271827, 59018382733, 18408479}

    Returns: 0

  135. {422532146255, 477778426, 430168720, 467516742, 1012235679}

    {176653017, 895671480422, 989282053272, 95092958604, 68995253}

    Returns: 0

  136. {587809316009, 54454431958}

    {217810551345, 65204324}

    Returns: 0

  137. {255495770673, 306646865853, 172275958}

    {118818179602, 198803254, 348585760029}

    Returns: 0

  138. {313956580020, 235521335, 311456702}

    {286449059785, 881420935532, 138735684}

    Returns: 0

  139. {244651605196, 411516942, 368751088476}

    {116854584790, 787277945263, 96737395}

    Returns: 0

  140. {353892625, 264082689, 37675490315, 336877536, 537921812660}

    {69809216, 180773586, 198886576, 61080520, 99452919}

    Returns: 0

  141. {654826192368, 436688070, 19522819}

    {165063427, 125125387, 680420579585}

    Returns: 0

  142. {207837092777, 528541724}

    {194478804, 139532041}

    Returns: 0

  143. {243201241385, 527463247}

    {58730166018, 157816463}

    Returns: 0

  144. {440422239249, 578516555374, 547493938, 974834234129, 281029825}

    {460162587714, 91176943, 424634184954, 14172212, 184766947}

    Returns: 0

  145. {401158250, 113920546, 803782179673, 70962437461}

    {628057270843, 36066569, 46870273, 805837237745}

    Returns: 0

  146. {487992591, 839024676490, 572832777}

    {570613674462, 68869645, 512250522449}

    Returns: 0

  147. {144895586, 105468699, 200762241221, 514805273, 633561703574}

    {943480017105, 14534847, 605070164687, 61963113811, 87149444}

    Returns: 0

  148. {700662609632, 2010801, 175644374}

    {185412906546, 573773292042, 572483065848}

    Returns: 0

  149. {755326463700, 610023967921, 517651730, 17742396, 108569235022}

    {180480804329, 64636745030, 50543654, 89059210, 832841339448}

    Returns: 0

  150. {304981543189, 287488687784}

    {504965511209, 98962973}

    Returns: 0

  151. {35188299, 398039651, 221121272, 580240073, 208486131}

    {706203689051, 52658892, 133001140, 948155946077, 163371079074}

    Returns: 0

  152. {400523950, 141299779309, 18790893097, 72404462260}

    {932638683547, 158503693457, 115586936750, 27056692}

    Returns: 0

  153. {234031193, 103621867, 189505561132}

    {7692734, 893628319964, 89593799}

    Returns: 0

  154. {240666055, 886563454456, 262086705}

    {56430195835, 148649151, 181656196}

    Returns: 0

  155. {260698435, 328120033, 562056353, 277460495292, 25891435}

    {293589746146, 11956885, 83557697, 572016883815, 142945222}

    Returns: 0

  156. {448365805, 436999491, 374777559839, 483867094, 739912716828}

    {6357321877, 82002944308, 186083654, 101633945, 122838530}

    Returns: 0

  157. {449142941353, 347434840, 125070530}

    {104273916, 11936729, 73492688}

    Returns: 0

  158. {644280613093, 401900570, 98546850992}

    {310668402359, 411515247267, 69008346}

    Returns: 0

  159. {376527363773, 129565820}

    {427801879370, 465769113877}

    Returns: 0

  160. {981909292}

    {33567948}

    Returns: 0

  161. {685758599}

    {306440858}

    Returns: 976505441

  162. {728649149}

    {275116474}

    Returns: 0

  163. {580504382}

    {330476968}

    Returns: 460839730

  164. {552753569}

    {353597576}

    Returns: 994095673

  165. {970478700}

    {336354}

    Returns: 770618818

  166. {658132317}

    {388618065}

    Returns: 0

  167. {492184797}

    {492527400}

    Returns: 889460710

  168. {840312821}

    {123505518}

    Returns: 355384521

  169. {727558897}

    {237415590}

    Returns: 336752778

  170. {699284359}

    {301155392}

    Returns: 0

  171. {669135456}

    {322646321}

    Returns: 349940270

  172. {967621719}

    {128107700}

    Returns: 0

  173. {922261055}

    {67377077}

    Returns: 370690164

  174. {860452692}

    {194797505}

    Returns: 0

  175. {2999999, 2999999, 2999999, 2999999, 2999999, 2999999, 2999999, 2999999, 2999999, 2999999 }

    {2999999, 2999999, 2999999, 2999999, 2999999, 2999999, 2999999, 2999999, 2999999, 2999999 }

    Returns: 637248194

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