Problem Statement
Aqa Asadi is a kind teacher who puts a lot of effort into helping students grow and make friends.
N students stand in a line. They are numbered 0 through N-1, in order. Student i is A[i] seconds old.
Aqa Asadi came up with a formula that measures how difficult it is for two students to become friends: for students i and j, the difficulty is |A[j] - A[i]| / |j - i|. In the formula, |x| denotes the absolute value of x.
Find the pair of students with the smallest difficulty to form a friendship, and return that difficulty.
Use the following pseudocode for generating the array A[0..N-1]:
for i = 0 to N-1:
if i < length(P):
A[i] = P[i]
if i == length(P):
A[i] = B0
if i > length(P):
A[i] = (A[i-1] * X + Y) modulo 1000000007
Definition
- Class:
- AqaAsadiMinimizes
- Method:
- getMin
- Parameters:
- int[], int, int, int, int
- Returns:
- double
- Method signature:
- double getMin(int[] P, int B0, int X, int Y, int N)
- (be sure your method is public)
Notes
- The returned value will be accepted if its relative or absolute error does not exceed 1e-9.
Constraints
- N will be between 2 and 500,000, inclusive.
- P will have between 0 and N elements, inclusive.
- P will have at most 100 elements.
- B0, X, Y, and all elements of P will be between 0 and 1,000,000,006, inclusive.
Examples
{11, 0, 30, 20, 1000}
0
0
0
5
Returns: 3.0
The best pair are the students i=0 and j=3, their difficulty of forming a friendship is |20 - 11| / |3 - 0| = 9/3 = 3.
{47, 1, 10, 3, 2}
0
0
0
5
Returns: 0.3333333333333333
Students i=1 and j=4 are the best choice here.
{}
1
1
1
500000
Returns: 1.0
{}
1
1
0
500000
Returns: 0.0
{922775522, 652913942, 199433255, 787328317, 969451951, 797384855, 334639666, 226448392, 822018246, 29395346, 802722515, 918324184, 274902223, 571486952, 802538779, 483667018, 546156066, 547778296, 77065150, 564653974, 190994759, 893170529, 389474108, 250200939, 85138230, 866155174, 437059941, 74418143, 20635319, 729041165, 492812116, 789041310, 80788342, 657551148, 83578153, 337344217, 358755901, 279590855, 586625340, 346220583, 656234093, 784279361, 209417013, 627709215, 531085527, 766358728, 81584560, 139917860, 539897052, 902664892, 22331841, 887434354, 972770284, 81553842, 656642132, 776167496, 800880463, 144114994, 803958154, 325218585, 629074313, 995579032, 915143235, 136723743, 296097141, 488631682, 126018575, 555421745, 695694510, 959479412, 370293222, 750454906, 547290356, 764543353, 345043918, 539777544, 935869071, 764495018, 21523167, 608660880, 226830175, 593435378, 581910485, 554000981, 981755478, 230975814, 482047251, 896754453, 484890024, 531623992, 651071307, 852013294, 415167693, 645121012, 905870749, 711116633, 579307283, 819164963, 286037053, 893339753}
21127135
944574999
717701653
100
Returns: 2169.5384615384614
{522109837, 374402083, 594553528, 566309265, 705832458, 585236063, 396646402, 313940406, 929409876, 747999710, 326501601, 527377660, 179617974, 230134508, 417657603, 761961673, 328027347, 187393545, 582507310, 410407852, 343346452, 423598349, 136088456, 977326863, 849776995, 979531651, 337690042, 594065795, 525165097, 270250492, 544598733, 989250948, 809362168, 60422977, 986538363, 398255223, 985553243, 598083254, 547587273, 495782643, 336009718, 669655234, 934171588, 987723810, 885228008, 311913165, 800564414, 53789888, 476194475, 97869064, 557976460, 149843952, 379125517, 358962679, 464126243, 72750481, 118865813, 613652047, 520257506, 786716860, 626442911, 524027909, 978049918, 791889535, 382537360, 862458421, 31590684, 588624552, 367359495, 210909241, 994426995, 932486252, 913420386, 604154827, 486369163, 3558013, 604363088, 779037721, 881878313, 938388910, 784711831, 569810277, 968667335, 932316060, 511989924, 793454468, 573850151, 468833573, 47115355, 623480792, 390737348, 700112711, 54312362, 171610790, 520964933, 50175008, 809577343, 814728131, 225399886, 930649520}
849003642
603700015
689566911
500000
Returns: 2.0524187755269583E-6
{989376828, 894348165, 154015031, 949014134, 587313720, 719709660, 622696149, 753302466, 541469406, 761264940, 891749187, 698857208, 637668931, 749998783, 831187508, 317235870, 611460176, 513942952, 351541305, 606511546, 394123236, 865817100, 64241900, 934720738, 138765108, 421159254, 147286813, 977430619, 160913006, 324667270, 378446562, 895881643, 447153307, 578111900, 416838017, 382397735, 245828727, 781499382, 868880760, 304337426, 821399435, 380753187, 351642192, 920703531, 677428434, 535072681, 939628565, 280430030, 942535151, 883414936, 423260941, 862149833, 568238916, 532704984, 644693798, 83069930, 605651964, 538624865, 393363870, 901700967, 728187629, 577005210, 629924515, 138198243, 527684669, 64321424, 375454215, 670268136, 813396453, 558946025, 290044752, 345449759, 82565990, 422679514, 421053255, 32077994, 701807758, 478188430, 908279157, 11807620, 419456560, 60613107, 677155355, 834460178, 580671815, 651180127, 612136105, 221140204, 362659516, 209130342, 773242432, 759569414, 9735635, 153167268, 655163013, 105892844, 317818739, 286985821, 36229019, 659386960}
824785523
383498744
467572837
500000
Returns: 2.0729684908789387E-6
{866709283, 414294240, 4648538, 917858268, 173827715, 145355254, 139917893, 192664519, 563594408, 69497432, 456996765, 280402221, 95719880, 266067786, 945954881, 286370802, 898688268, 426631624, 120575299, 511443236, 149932751, 16863840, 578534616, 597147345, 841613963, 862786864, 251850852, 651967440, 87832919, 84116780, 921122394, 921405806, 379911714, 390768084, 433276943, 75368243, 214932214, 551054774, 488936773, 821720211, 302993882, 95646403, 769112803, 857478515, 764596129, 53199459, 668627245, 97004701, 113908552, 787854269, 989782897, 865627711, 56114841, 997619292, 825261354, 798422118, 797470846, 467392947, 266470234, 721717805, 243793074, 331219979, 695659847, 70646223, 967799246, 557356439, 715522481, 341846249, 550605408, 612015541, 581867252, 877306740, 542883605, 237408936, 355737348, 765630714, 799252428, 882371878, 520819267, 376398341, 640340562, 551415944, 975577912, 732809033, 358181702, 210143254, 355454791, 678479575, 383236409, 89747159, 450714777, 524058850, 673986911, 839756485, 789361094, 460373213, 534888137, 54210779, 843262895, 974263673}
800567404
872125476
245578763
500000
Returns: 2.0931011386470193E-6
{744041738, 934240323, 974175518, 591735133, 346480981, 865968122, 362172377, 632026579, 175653938, 787795401, 22244344, 451881770, 553770836, 785932060, 359484779, 841645007, 182121090, 753181032, 184576561, 121407658, 909537538, 167910586, 801655329, 554541220, 130602076, 595586471, 61447623, 326504261, 723580836, 138533559, 754970224, 533069233, 308874857, 908457008, 154748601, 59510755, 180240436, 25642899, 814025524, 339102990, 788383600, 515572359, 481550675, 85425496, 142935821, 981391714, 807691395, 323644843, 871421232, 573400135, 560100109, 574138321, 249023504, 171361589, 415894373, 99913565, 989289729, 687333032, 848404601, 127873908, 345537791, 384197280, 56362440, 711922206, 116741812, 50391446, 350558009, 718457100, 996642366, 668880321, 877485015, 999098251, 417061948, 347105627, 704282175, 794150696, 486631628, 286555319, 842187379, 449817058, 271290028, 42218774, 274000461, 926125156, 426863593, 359040917, 102568741, 725753475, 403813301, 261535981, 833219860, 288548285, 924377452, 526345695, 923559174, 811058317, 751957535, 821435744, 359124760, 997968381}
362488550
651924205
728617429
500000
Returns: 2.119003220884896E-6
{123456}
234567890
345678
456789
10
Returns: 8333191.571428572
A = {123456, 234567890, 958968621, 353106369, 103025544, 664206330, 514591322, 898217931, 176235549, 752137571}
{938716038, 696783525, 73140996, 471863629, 129437551, 97516501, 729265849, 950312638, 912445208, 328696749, 924491846, 599211006, 345001271, 630842356, 275744218, 630486447, 800804380, 661000816, 365477197, 935981446, 175354133, 443485748, 213038695, 404258097, 394502228, 723081699, 413729058, 164547177, 242105682, 38711469, 187795347, 854208998, 244484201, 118201200, 326359828, 41087751, 742062740, 473669299, 416181809, 673608766, 190410887, 723081530, 73957938, 146029991, 86658150, 448721832, 612832342, 648673283, 444529010, 419230399, 594868091, 403727803, 390834798, 73225780, 268670849, 99087698, 899950576, 225414110, 788246869, 571410208, 888044579, 908402119, 807824572, 638675457, 595068641, 30705464, 84228812, 94790970, 461874807, 792380380, 533646686, 60405756, 789269977, 481007056, 489626830, 840687774, 497760758, 211580551, 502800309, 807780803, 249068122, 61064441, 352125864, 686217034, 202982397, 776480261, 805979905, 727641241, 685724325, 920651890, 551785262, 265589975, 37923011, 205877539, 395147856, 824840696, 225901159, 584964632, 104147790, 896984004}
830874179
525792547
881803330
500000
Returns: 2.182438788048092E-6
{111015754, 216729600, 923774510, 149535759, 10918814, 523162101, 955315596, 389674691, 524504739, 341961980, 194772157, 475723287, 508084960, 150706623, 980446127, 894588647, 793065205, 987550223, 429478460, 545945868, 226130917, 594532495, 436159407, 66684704, 683490348, 160914038, 223325830, 839084005, 169025596, 798160986, 726675915, 170905157, 878480083, 930857392, 342798754, 734058266, 2338224, 948257431, 741270561, 482163548, 675800605, 143007478, 491428549, 79009712, 170030581, 671881349, 341831022, 170280686, 615902418, 618636999, 870218043, 702172949, 288776193, 952000824, 449238404, 109407148, 386736720, 445354196, 75213961, 682599050, 698617293, 662616888, 463494434, 984984172, 35183211, 523740479, 133125075, 471401822, 199083761, 845449896, 825469186, 182197266, 663448320, 295736479, 133138918, 869207756, 595205428, 615763999, 529201153, 172371517, 174984856, 551867278, 650548421, 879533157, 980492291, 335443388, 549298591, 479947873, 1268478, 797473443, 934290346, 325046679, 997141555, 597499488, 529345936, 880558533, 734142562, 647156859, 914976930, 916893448}
806656060
10624008
364841988
500000
Returns: 2.1496407950231515E-6
{283315477, 31642943, 483236013, 118379892, 892400084, 952602966, 472537340, 829036751, 136564269, 355227210, 760019742, 647202836, 257307913, 666775634, 804041496, 449862844, 371465294, 900238895, 198512454, 742049562, 276907700, 36751239, 954247387, 732906583, 382543932, 307574380, 36717865, 222448822, 804773512, 852577764, 269351741, 491396588, 811238490, 448546308, 64270412, 718200778, 967646453, 717812824, 771392044, 999546334, 452362320, 149072699, 908899160, 306956700, 257198276, 898836129, 775862440, 396920828, 82243087, 109215597, 440535256, 119511555, 67824121, 711882393, 334838691, 410898601, 287383599, 665294282, 948320332, 797583156, 800362010, 715594189, 529229766, 212399413, 475297788, 16775486, 768160610, 142979934, 645120719, 193486673, 121086942, 9021508, 832593931, 114261165, 772855750, 897727737, 987617366, 19947440, 141741262, 245790234, 104696853, 42670108, 948970977, 72849273, 344141443, 193169047, 296412541, 527221772, 21845371, 678090261, 320590687, 384503382, 952564828, 992916701, 958511284, 235038894, 951211960, 119414549, 16978060, 645630889}
73609938
790422744
142847914
500000
Returns: 0.0
{455615200, 256621758, 38902251, 87224026, 65053343, 378248560, 698587087, 268398804, 158689271, 368492440, 325267321, 519919852, 715358869, 186639901, 508743398, 5137041, 363726119, 517960300, 967546455, 352013983, 36512480, 482765253, 468540096, 395333190, 671532052, 749201990, 846314643, 602018382, 440521421, 612027275, 398166838, 106855279, 743996898, 261202492, 494570072, 411171286, 522889205, 192400948, 391448057, 221961845, 937752038, 568998654, 621337032, 534903689, 635537975, 827028378, 501065856, 918528238, 253616495, 308622198, 305819736, 122989432, 965765524, 590657429, 220438978, 126250782, 479202482, 590267100, 821426696, 617599994, 315967455, 764776226, 889932366, 558708128, 620445097, 218638496, 403196138, 224623518, 87362406, 541523457, 412909442, 835845758, 292911539, 223957856, 707539842, 631280450, 85062029, 14065417, 459314110, 905348223, 30613587, 242300941, 952426265, 971198135, 121651329, 47099442, 629665762, 984561143, 42422263, 558707079, 703095771, 148992818, 613020833, 974473179, 383881361, 880691266, 168281351, 591672246, 827807200, 960507601}
639326355
570221473
625886579
500000
Returns: 2.034501069130312E-6
{332947655, 776567840, 598363761, 761100899, 946534613, 98861422, 920841571, 707760864, 770748808, 381757670, 890514906, 691399401, 878442557, 407741643, 332338767, 560411245, 942126215, 139476968, 736580449, 548117677, 87289263, 633812000, 691660809, 57759797, 960520172, 190829594, 655911414, 276555203, 662408603, 371476785, 940842670, 718518714, 381788037, 778891416, 511008998, 395313799, 488197428, 372021812, 716536808, 30516627, 714313752, 283891871, 624946908, 467883409, 722705669, 50187888, 935097274, 440135641, 11129168, 799200803, 581169688, 126467310, 158674180, 350538999, 401006533, 136570232, 965988633, 810207186, 698328324, 728788837, 417712172, 522786260, 955667698, 199984103, 60559667, 711673510, 747059669, 896201638, 824571368, 889560241, 708527206, 662670000, 462057151, 333654547, 347256666, 364833163, 477473967, 418248865, 780682222, 978766940, 251497589, 733103778, 250848815, 164514250, 899161223, 901029844, 667951716, 736867774, 357966424, 144356628, 85600848, 913482260, 863411375, 366095121, 518079441, 645237098, 676522753, 358897204, 634841069, 980417045}
615108236
353815466
403892505
500000
Returns: 2.2073057405400395E-6
{800214646, 591481183, 154030000, 729945032, 828015875, 233335019, 733030583, 147122917, 382808339, 395022901, 455762485, 567911682, 336493507, 927605917, 37040669, 115685443, 229354301, 52165640, 800581711, 863114838, 843098786, 781063483, 914781521, 15153672, 958336288, 628661940, 760475453, 954887294, 3189244, 130926295, 774690499, 744042876, 605718448, 886514868, 527447924, 674423579, 748472919, 141577205, 746658292, 252932145, 904736202, 994989830, 337384780, 695830398, 809873364, 978380143, 369128686, 666775783, 182502576, 998607403, 442658905, 838773191, 642754847, 229314035, 286606820, 851922420, 157807508, 325114533, 571434688, 843772943, 228284886, 571968297, 316370291, 841260086, 504469508, 499675786, 87127929, 272812482, 270608319, 942629757, 709177702, 75633507, 336235494, 148383970, 695801494, 688320413, 578713901, 117399573, 393222331, 52185650, 886242325, 223906609, 549271371, 62863105, 262810375, 463788235, 415065666, 489174406, 382338581, 319940714, 468105932, 677971696, 527662644, 347651599, 652277522, 290889463, 893592151, 126122163, 445670202, 709154485}
882062121
133614195
181898431
500000
Returns: 0.0
{677547101, 402599263, 4663506, 112649894, 669135, 658980619, 664113062, 586484977, 699900608, 408288131, 726042803, 739391230, 89511724, 443674921, 446775310, 84820375, 512787129, 673682315, 864582973, 768046528, 602703566, 932110230, 842934965, 677580286, 952357140, 70289543, 570072224, 334456847, 225076425, 476515077, 608538328, 650673571, 948542326, 695375788, 252714846, 72426819, 8748402, 616165337, 71747036, 65282192, 681297917, 414915779, 754855391, 632605382, 893245795, 201539653, 803160104, 188383186, 353875984, 489186001, 12976118, 547283801, 835663510, 989195611, 467174375, 862241869, 349626391, 253882615, 858401787, 958757049, 330029603, 624945598, 677072891, 482536062, 649616818, 701538796, 722163463, 354456066, 7817274, 999494537, 295967463, 902457757, 800348373, 261875924, 630485586, 421873126, 676158572, 521583021, 710795179, 711743639, 107126320, 714709446, 843898663, 256179228, 40320262, 612685898, 453351620, 950309041, 697882741, 200557532, 145578277, 446256395, 483085917, 34240809, 786475602, 641574568, 110661543, 598379860, 547671339, 729063930}
857844002
618445663
959904364
500000
Returns: 2.12714815374176E-6
{849846824, 217512606, 269157748, 81494027, 882150404, 379593481, 181334807, 730879769, 603132143, 421553361, 291290381, 615903511, 252595412, 963539195, 565337947, 640094579, 91187218, 291403720, 633616967, 964150221, 653480349, 83156969, 357227675, 343802158, 241345253, 511917153, 84701728, 8993668, 860824342, 235964588, 446181421, 971165002, 881300733, 508031973, 974186511, 351536599, 974056632, 94548726, 691803056, 578869713, 461654896, 129808995, 758465267, 565585102, 980413489, 838559904, 237191516, 415023328, 820216660, 983559870, 583293337, 845728947, 319744170, 867970648, 57807395, 872561319, 836412542, 178855433, 731508151, 69945884, 140602316, 379160367, 742808223, 123812038, 89731388, 489541071, 357198991, 26034179, 453854232, 347531314, 296617958, 729281999, 969493984, 371572615, 565169678, 450393107, 68570503, 925766469, 32163285, 785162355, 738075792, 914340279, 847353952, 453290615, 109002153, 171649024, 196670306, 997582940, 13426895, 77379085, 823050629, 210745831, 438509190, 720830026, 920673682, 996054936, 618902945, 365604818, 649672476, 457801370}
128593144
398244393
446738286
500000
Returns: 2.1089838494016815E-6
{727179279, 442491421, 119791255, 50338161, 54803664, 514067078, 407384554, 465209090, 215191673, 434818591, 852742703, 783587796, 710646369, 479608198, 975072588, 195368776, 378415311, 912920395, 402650961, 574114643, 704257133, 525375720, 875315655, 6228765, 530333373, 244716761, 189265767, 687325760, 787744255, 995414105, 280029250, 582828429, 105231137, 25720889, 695658168, 44507107, 529299384, 569136858, 721924540, 801285231, 943249349, 840906955, 470903139, 793532091, 67581177, 61719414, 966190202, 936630738, 991590068, 179171199, 153610550, 263067552, 512652834, 332884949, 529546954, 587913500, 737059421, 398795519, 899581783, 184929991, 947379773, 723309672, 103510817, 56260018, 529845965, 982576086, 406095254, 402645031, 191063187, 695568098, 592235722, 851073509, 134844324, 186302038, 499853771, 478913088, 460982441, 624917178, 644703401, 858581072, 667787790, 405143109, 145776501, 351639470, 181479308, 29374683, 238751523, 454922304, 34003788, 957995910, 205555706, 975235273, 688899732, 407419236, 346043759, 346740033, 541005075, 837862516, 165534342, 772678082}
690514298
178043122
929776951
500000
Returns: 2.183983104706702E-6
{194446263, 962437503, 679252764, 724215034, 231252194, 234679940, 924606305, 609603882, 532283943, 448083822, 417990281, 660100076, 459869322, 999472472, 93635218, 750642980, 661848139, 530641799, 171684955, 479046333, 460066648, 676422467, 98436360, 963622647, 229386957, 96409835, 998862545, 66895313, 423492164, 754863615, 818909819, 903319860, 743022283, 838377080, 7064355, 733682358, 494607607, 748757722, 47013284, 318668010, 428639060, 555800171, 888373750, 21479072, 445920876, 579846199, 105254346, 458238141, 749102741, 673545068, 723927770, 266545430, 410594229, 506627253, 415147241, 889404954, 928878304, 618735605, 481516143, 299914097, 757952486, 481319705, 169246149, 402568732, 383821270, 475611093, 336098050, 779255882, 928272149, 748637614, 884058222, 382930484, 303989935, 295998728, 848398598, 507433069, 558427111, 29100619, 257243510, 223171786, 593704523, 895945946, 444199057, 544955593, 664021934, 883305085, 277037477, 207228935, 349547948, 133579989, 588060790, 34691970, 353151001, 94008446, 480241839, 406253133, 49246470, 605087474, 267535479, 501415522}
666296179
961637122
707782877
500000
Returns: 2.089396937361969E-6
{208311185, 290825134, 431539136, 700614056, 134041084, 656310604, 881068322, 748057541, 635034373, 874120235, 999751785, 291958746, 728086812, 222573248, 670359685, 718086791, 760635861, 493835969, 272879679, 534949213, 49035689, 197458828, 265070284, 893957866, 864606721, 699639559, 691255389, 802166418, 435913020, 434638327, 595580702, 521214078, 320111543, 226362025, 629733744, 328539040, 588494535, 102140740, 190460635, 286370181, 547662550, 780418126, 838388080, 733821766, 161231472, 610246679, 368784742, 550164220, 824777330, 626606243, 976292752, 377905194, 524944823, 2026530, 901854605, 651983265, 439248887, 386149417, 403510661, 182031558, 379261637, 324448701, 935558120, 223960651, 778426871, 35381801, 444999976, 847838314, 920275667, 211573297, 910560466, 433489860, 217480295, 916032820, 647924073, 66715916, 621495481, 138930197, 724782674, 680438143, 750028291, 494940234, 433115995, 554120063, 664824945, 542815493, 254391451, 746362147, 943162770, 862367289, 89577010, 415428289, 484497912, 254854481, 880653788, 825212795, 222636640, 586701426, 678357200, 981213087}
139600448
980217188
366441157
500000
Returns: 2.1008006151144203E-6
{85643640, 810771217, 282172642, 374490922, 15522346, 81956197, 402085330, 187419594, 247093903, 887385466, 561204100, 459643030, 186137761, 33609520, 375061587, 273360988, 749101421, 111557373, 41913673, 436085639, 804845212, 348505575, 488190996, 851351742, 862422837, 432439166, 500852161, 476703239, 366628197, 194087837, 138256527, 841705509, 957902690, 39018209, 351205402, 312681552, 848770026, 871696140, 515549386, 799957703, 738084999, 200344074, 547030688, 961768754, 953431906, 542234192, 93988157, 71771623, 996150738, 826012843, 841577232, 381383072, 717853486, 175768834, 78626889, 662302714, 631067770, 606089503, 981649764, 297015665, 189834350, 373630738, 1293445, 570269365, 218541441, 823384084, 785068243, 224449159, 657484622, 559610081, 206178223, 260314102, 677797910, 25729503, 287640897, 95235897, 718940151, 543113645, 337322783, 48824121, 675945025, 280710332, 731538552, 452468917, 442334832, 105573884, 997710144, 203701511, 963739663, 37951367, 767049362, 183712988, 148749181, 355304426, 14851861, 179693156, 730878043, 58959117, 190423801, 709950527}
406554333
760015917
144447084
500000
Returns: 2.208363514301362E-6
{552910631, 625684560, 132806149, 343335055, 893208352, 511397062, 919307082, 921748922, 859153441, 195617957, 126451679, 336155311, 644188717, 258506526, 198656956, 242495920, 36329506, 438106781, 105914936, 341017329, 855621995, 499552321, 711311709, 513778349, 856443689, 284132241, 605416200, 860068063, 2376107, 953537354, 972104363, 162196932, 181833094, 556707132, 662611595, 5652060, 814078249, 51316997, 545670870, 317340482, 514646714, 620270030, 259468560, 894748475, 745632332, 470426440, 528019576, 298411765, 753663411, 316591441, 411894445, 384860950, 201934146, 640683143, 259194444, 668826899, 117853914, 531062321, 563584124, 117032503, 701644539, 426608039, 361996046, 502717345, 658656018, 316419091, 420103771, 306092743, 103521573, 907646865, 498000723, 382105612, 846943521, 549286929, 222324990, 828788618, 111352082, 242264354, 658690896, 118447574, 605657023, 771513170, 29961101, 645785040, 805983990, 959504286, 35996091, 956008149, 279283816, 209740189, 149554439, 948202431, 104172454, 336860904, 440221945, 235410992, 947947441, 826184082, 1252934, 729859971}
382336214
834781914
922453017
500000
Returns: 2.1847226713041045E-6
{430243086, 145630636, 102333123, 17211921, 69656876, 642075395, 141561558, 66143707, 176245703, 913915926, 691699264, 507634860, 807272406, 69542797, 903358865, 797770124, 614729603, 350795453, 169916198, 950981757, 615226775, 941771072, 934432421, 180000220, 145431802, 725759851, 415012971, 534604884, 929296027, 4158862, 100919453, 773860367, 114591501, 369363317, 92911249, 989794580, 74353733, 820872397, 165726883, 834723267, 36425, 331367982, 971906439, 122695456, 123972024, 693585957, 257018255, 820019175, 925036819, 515998042, 687244397, 802199563, 394842809, 814425447, 144794731, 679146349, 18500792, 459830403, 731657756, 523188613, 512217252, 475790076, 427731378, 143993321, 803803327, 813249369, 763967302, 977670862, 840730535, 960716381, 793618486, 913962594, 16089125, 658983620, 865837085, 152275860, 503764021, 646447802, 271231005, 191866291, 531573756, 967348739, 619555661, 544133895, 583493877, 522262677, 783110048, 3282042, 594827977, 795389746, 827026791, 712691866, 354562995, 23450114, 574420026, 881063365, 456188836, 593409040, 103254071, 458597412}
653085363
323408639
700458943
500000
Returns: 2.1351416559731656E-6
{602542809, 370609450, 952966636, 986056062, 951138145, 362688257, 662578573, 800473035, 788305241, 927181157, 256946843, 384147140, 851462627, 294439803, 726954234, 648011589, 901957695, 972312128, 643982931, 147085444, 666003558, 92817812, 448725130, 842426834, 434419922, 458559458, 224609742, 209141705, 565043936, 58575640, 348628017, 94351790, 752382647, 182019501, 109350175, 977732356, 334629223, 295460522, 490815634, 643278050, 776598147, 46261199, 389377043, 59470441, 211139719, 916745474, 396082406, 46659310, 391377488, 6576639, 843700882, 805677440, 583956209, 279339748, 30395018, 689465798, 210319675, 974737757, 313592116, 343205451, 613961969, 233800109, 83401239, 490302036, 952745901, 306284377, 399002830, 354281707, 577939490, 17581154, 794268982, 35754097, 890267475, 768680310, 505553910, 885828580, 601208691, 50631243, 588803853, 556457012, 752457758, 461946833, 328043682, 446278014, 361003764, 671160340, 821396002, 460621412, 910372137, 676006563, 918359871, 477181302, 309986269, 710039331, 708618106, 235543726, 673258234, 65666730, 914083211, 478506856}
215006509
103207368
187292865
500000
Returns: 2.1901103377588163E-6
{479875264, 476694797, 512428139, 368760923, 123791405, 497161854, 884833056, 944867827, 400364771, 235413648, 822194428, 846798693, 309513576, 105476074, 431656136, 203285786, 185390517, 885000800, 416812189, 757049873, 421813074, 948897298, 671845843, 799820710, 428440774, 900187068, 329173781, 592506529, 491963850, 818025157, 182475846, 706015224, 390173786, 994675692, 830821840, 666907600, 299937446, 770048654, 520937118, 865693568, 261987858, 757359158, 392986919, 992450168, 589479417, 844937722, 125081085, 568266720, 562750896, 205983240, 119050826, 809155318, 71832133, 453082053, 915995312, 404817979, 697105826, 194677836, 186698481, 163222289, 424534683, 577949414, 149136571, 426545280, 392860471, 799319391, 739071097, 730892559, 23976441, 365617938, 381058743, 858783082, 59413079, 583409733, 440238002, 914348561, 702448625, 749781959, 910171965, 924842997, 682169755, 952749670, 626466238, 639594137, 724652923, 230123467, 154649217, 507895312, 930949030, 851590649, 300864948, 536638005, 974237545, 396628541, 842816186, 291261562, 890327633, 537924428, 16084341, 88350829}
190788391
588038837
670331530
500000
Returns: 2.106979791956815E-6
{652174988, 996640880, 363061646, 337605057, 5272667, 922807454, 110882797, 384229880, 422489773, 953711617, 92474739, 428343706, 472597264, 330373081, 255251505, 758559990, 177651341, 211550200, 480813451, 953153567, 181417853, 686083309, 894966555, 462247317, 717428894, 46847404, 138770552, 972076089, 422679027, 577474667, 16323676, 26506648, 319136929, 512364609, 261121493, 654845376, 855180205, 539604047, 846025869, 674248350, 747377575, 177285107, 105424791, 220397149, 676647112, 776925235, 264145236, 89874123, 734124304, 696561845, 689368046, 517665928, 969773535, 331857089, 96562861, 415137429, 888924709, 119650654, 59804845, 569378400, 231312132, 40992180, 214871903, 772853994, 538007780, 1182394, 82934621, 107503403, 761185403, 713654722, 381709239, 980574593, 523525958, 401934420, 374922094, 942868542, 799893295, 448932668, 522712074, 998261714, 608086489, 148585232, 924888794, 537942992, 502162810, 87849126, 901763173, 260201943, 660353919, 437240199, 978337300, 6160173, 224628079, 83217751, 977014266, 645741930, 398569028, 600116654, 531946213, 817088276}
166570272
367837566
448337456
500000
Returns: 0.0
{824474711, 811554223, 627555887, 306449190, 177925934, 643420316, 628104548, 823591941, 34549303, 966976847, 657722325, 599823254, 930648221, 846442091, 959953414, 22662183, 756051438, 124238873, 249847445, 858085256, 232194637, 837130056, 409259264, 833501927, 711449746, 779647018, 948367331, 941580178, 54631673, 336924178, 853966776, 638170082, 251895336, 325020793, 572527687, 638987888, 820488428, 14192172, 171114614, 896663868, 228972022, 892178330, 522895402, 448344138, 763814807, 84744, 993143922, 316514265, 491636977, 895968445, 259685259, 524939070, 748821463, 91738658, 277130416, 130489610, 80743585, 339590740, 641739212, 684362506, 41884845, 385141485, 575574503, 414129970, 978122357, 494217409, 717970156, 484114255, 207222354, 766724238, 677327003, 807398835, 688876305, 511631111, 723466922, 676421256, 897337965, 148083377, 135252183, 362852428, 828970490, 934355338, 928344083, 731259114, 279672697, 941779528, 645081859, 717541314, 975898079, 317857016, 360842377, 774444879, 180051352, 769806968, 111212339, 996427035, 320671158, 72374344, 633947350, 836997720}
433524157
442603563
226343382
500000
Returns: 2.0448852308164204E-6
{701807166, 331500298, 478189394, 275293324, 354374464, 777893913, 854154295, 262953994, 646608841, 275209339, 928002642, 476335535, 388699170, 71339090, 369688048, 282969119, 43279523, 741960284, 313848707, 468049678, 282971420, 988176803, 632379977, 495928534, 705470598, 221274621, 52931363, 29977727, 690379589, 391340956, 687814605, 253628774, 184653743, 842709717, 293999345, 331958396, 84559175, 197608300, 787375369, 709013915, 714361740, 603276283, 235333274, 381323858, 142154498, 223244261, 427175334, 838121675, 663010385, 681514311, 830002478, 233449680, 646762859, 970513702, 867763442, 140809060, 567529735, 559530826, 514845576, 504379344, 143629563, 434323522, 641309836, 55405946, 418236927, 987252423, 58038415, 860725107, 649464047, 114761015, 969149503, 634223077, 858021916, 326360533, 658151014, 704941237, 584717164, 552266825, 456620295, 731238412, 754887224, 133986164, 226766632, 924575237, 348354588, 795709923, 683367813, 764815213, 291442233, 489645838, 743347461, 833901583, 135474625, 456396178, 241615155, 55940128, 537740556, 544632042, 735948487, 565735161}
999240574
931230295
4349308
500000
Returns: 2.038249795665458E-6
{874106889, 556479113, 328822900, 949170197, 235855727, 498506775, 76408772, 702316054, 254873107, 993507308, 784422225, 647815084, 551782858, 882375368, 488250685, 838243324, 621679620, 363476952, 82882701, 369186104, 747608939, 135428279, 150467950, 158355141, 994458718, 367934963, 567560873, 704514555, 912266770, 150790466, 521662434, 570324940, 113616886, 655365901, 310438271, 316100908, 49867398, 672196432, 112464114, 222601430, 785890723, 318169499, 943975889, 609270847, 229322193, 151436510, 861206752, 359729078, 129351054, 585953644, 400319691, 236927557, 839671522, 730395271, 48330990, 442300513, 468176614, 484503644, 387951940, 910535454, 954202283, 192333555, 296979697, 987853933, 272212232, 70221959, 988041218, 237335952, 386673002, 462797799, 264767259, 461047320, 27167521, 436057224, 297867838, 733461218, 682161834, 956450273, 774193143, 804657129, 684599222, 624789001, 816361192, 117891353, 420831743, 358468314, 725449031, 517121845, 606986394, 75295388, 420819806, 598391018, 94693163, 851813391, 670780504, 701592500, 45981952, 603029004, 546777620, 585644605}
975022455
711029024
782355241
500000
Returns: 2.0584729835713273E-6
{395176662, 551953051, 182772684, 465642378, 208255569, 691029368, 428129498, 450979559, 848969349, 527991865, 713785630, 862288416, 547649105, 526516820, 647101406, 918504050, 381044761, 24884858, 210433009, 937158685, 479942056, 863790786, 832471458, 724099247, 805859524, 661069833, 467385416, 744659999, 56030335, 474463680, 772641757, 315606978, 74811465, 12844534, 224616175, 133758302, 175999188, 266556409, 130040481, 292459816, 570193052, 608589731, 578219430, 953388904, 184678157, 200097534, 18774154, 406251953, 69611023, 178843181, 589790930, 537592311, 198387806, 99015152, 670507270, 611728729, 3419217, 564815631, 846575427, 13838314, 656599978, 84055640, 393195655, 772001793, 544552337, 779128047, 544693294, 717762572, 895020521, 883924663, 354441275, 939872697, 399845094, 743627345, 792618925, 995808283, 391084979, 582798944, 727688558, 371476359, 430010198, 751688093, 490310563, 401360205, 568553808, 873270751, 51083846, 994607918, 208284301, 34819544, 135446948, 585999892, 397428060, 948300900, 705958264, 481513875, 32129132, 257957166, 720600628, 32711806}
140231474
873681043
484557594
500000
Returns: 2.1918480786259743E-6
{862443653, 363071131, 33406190, 139519243, 89736832, 411642230, 945351250, 890341619, 461028879, 541257095, 984065948, 738800696, 5700055, 456446558, 765664043, 182606243, 959444857, 642606269, 274434271, 842090375, 235751571, 600976798, 55592164, 386525854, 94847637, 807730176, 276982187, 128024816, 986745519, 528880458, 315317582, 632303144, 712602611, 825500725, 946087840, 117900814, 731241947, 155005269, 455129233, 809842602, 51787499, 323482947, 995690041, 181335886, 563017855, 423257051, 747772840, 927859363, 240984431, 83282514, 160108143, 246102920, 977435741, 272757456, 851074825, 622048179, 195238100, 489788449, 428509787, 125027157, 467172692, 842065680, 458930987, 118310501, 984666914, 272163054, 179728822, 94373417, 632229476, 936994179, 941231043, 57868936, 568990705, 558356767, 727303018, 24328257, 488529649, 281949653, 49056663, 736067080, 64754927, 656351659, 493765851, 594676328, 346063695, 436029142, 794402539, 451947281, 523828462, 620469101, 812919299, 350489327, 766712069, 929857378, 840156344, 835994244, 249198530, 730214863, 822601765, 52621250}
407185359
653479773
967596260
500000
Returns: 2.1204995048633656E-6
{739776108, 883017213, 297900432, 108363377, 971218101, 546115827, 876433729, 38531668, 778121149, 554522325, 549313526, 910280245, 463751011, 267482830, 175398677, 737880447, 537844946, 264122937, 338435533, 448259532, 700389090, 752023545, 278712876, 48952461, 383835757, 245562515, 86578958, 507594376, 327526160, 288329969, 444132679, 247761835, 645361018, 343189642, 962526766, 810871329, 696550170, 924560669, 780217985, 32258112, 537177217, 743408903, 708127913, 114315606, 650185550, 646416567, 886836991, 449466766, 707325107, 577656382, 730425362, 544548066, 875377136, 446499761, 31642373, 337400360, 682024251, 709728535, 596583419, 240011263, 273950141, 891247717, 819633588, 54553745, 129814216, 60165330, 228625085, 470984268, 78266427, 285030956, 941881538, 179660447, 33103577, 376881454, 367019842, 757880977, 589769583, 686133101, 661596779, 809485797, 285638929, 147154489, 788393143, 787992450, 414745586, 289959536, 541516489, 204253913, 544405354, 501085918, 490391644, 409946031, 17102603, 321479320, 974354424, 891712080, 757439932, 497439822, 629635634, 72530694}
382967240
433278502
745602186
500000
Returns: 0.0
{912075831, 402963289, 148533939, 782240249, 143871361, 266728689, 688622741, 477893728, 95213411, 567787555, 405733109, 786792526, 626834699, 492379836, 293961314, 998187383, 530105771, 881844348, 812502266, 353191222, 751165874, 903070292, 501833588, 6346337, 377856609, 687190125, 896175736, 477098465, 549413342, 342746747, 277980508, 859425270, 869291430, 155845826, 687793688, 89981102, 251792922, 399148794, 105306729, 840812902, 22566927, 454506855, 711737789, 342262594, 737353245, 578404080, 615835670, 384934904, 878698515, 773267719, 296947311, 961886679, 654425065, 616446801, 913447403, 347719809, 873843133, 929668621, 883550518, 354995369, 84522854, 944225018, 885368920, 400862460, 569928793, 262028340, 158627881, 847595120, 815475389, 633067740, 528671299, 6484689, 202249188, 486578145, 301703934, 786400959, 982181521, 90316541, 979169627, 469043779, 211555663, 637957326, 86815693, 686341305, 192255473, 438857199, 874769711, 956560552, 564982247, 967842008, 872896728, 879468205, 972525883, 8068530, 399724502, 246192441, 974509330, 264664780, 440464767, 96235402}
358749121
216872495
523608112
500000
Returns: 2.0820927530679636E-6
{789408286, 217876632, 413028180, 754879647, 25352623, 692374289, 910877224, 917255788, 707272949, 581052786, 676013426, 954476810, 84885648, 303416107, 703695955, 553461580, 108505860, 89500282, 876503528, 963155651, 801942657, 345289035, 16126298, 377600947, 666844729, 128817728, 705772508, 565496021, 185161251, 102196257, 820656340, 179916693, 212115301, 673534749, 409265345, 487984349, 217101144, 873736926, 135428213, 63228413, 504161381, 169400072, 129208393, 570209583, 820725675, 506596329, 754899821, 906542314, 636211188, 267641581, 162231792, 965364557, 552366460, 85156366, 94014951, 358039259, 69457273, 149608700, 756656882, 466184211, 186267572, 698439787, 246071513, 42138436, 10043364, 755063354, 498696148, 224205965, 261512340, 981104524, 529321795, 833308938, 76427531, 301307568, 945216030, 814920940, 79626185, 789467257, 300537732, 542462496, 137472396, 128760156, 385238249, 174624689, 264732628, 706648329, 913055664, 708867183, 589354404, 553491558, 255401805, 647752905, 636777152, 989625015, 533922582, 891844813, 482750726, 736922477, 542465904, 116144847}
920670274
996671231
301614038
500000
Returns: 2.1287737837250985E-6
{256675270, 737822714, 263661687, 428756513, 201801154, 826847886, 136926965, 356617841, 24365211, 594318016, 536228273, 830989091, 129075870, 528313113, 113430589, 108735777, 100766685, 416049689, 354365518, 159259338, 852719441, 201368514, 239247010, 334994822, 660865581, 566650075, 515369279, 240032842, 817113903, 447785040, 359536901, 791580128, 144873708, 486190934, 425704271, 767094129, 891237370, 643292319, 755484232, 166750463, 284518360, 880498031, 841646272, 212017299, 612926102, 729755845, 483898500, 428149717, 807584596, 758220185, 732549012, 968842435, 745275123, 255103407, 979615246, 364563444, 261276156, 74581518, 629763246, 581168317, 996840292, 42589086, 606774113, 683414418, 864018676, 248098362, 547592411, 895784084, 998721302, 34174033, 529972291, 660133181, 536745146, 411004258, 584932854, 843440921, 472038123, 484822702, 913077848, 615881213, 772217133, 619562993, 683660805, 72973544, 333414519, 855545992, 660169614, 756141083, 904898564, 434108375, 346734885, 707209608, 592200426, 381246957, 668120662, 947562649, 699820124, 504147436, 353295037, 844882294}
191419417
481502692
79619964
500000
Returns: 2.036386147686869E-6
{134007725, 962801529, 528155929, 397600646, 374454421, 252493480, 654148716, 795979901, 636424749, 607583246, 806508591, 2468633, 292159558, 339349385, 231993226, 372837977, 679166781, 328738361, 418366780, 769223767, 317356952, 352415261, 462367722, 997421436, 949853701, 8277678, 619933318, 914569670, 747829081, 207234550, 193384731, 112071551, 73836851, 3879850, 147175929, 456269374, 446480122, 822913182, 80572977, 389165981, 766112814, 595391248, 845256147, 439964288, 991265801, 952915362, 622962651, 654789859, 978958004, 957626786, 7898956, 386181040, 229355783, 723812979, 160182794, 669850162, 453095039, 294521604, 506664874, 696152424, 803617741, 800599126, 672509445, 615862398, 304133246, 741133376, 477595207, 977427668, 735930257, 91038813, 116762052, 486957423, 705890757, 229528945, 519616947, 576993634, 569482793, 183973411, 525617957, 980471934, 993101134, 819193826, 687116094, 266289667, 110924406, 709476387, 698455568, 213480446, 220442718, 19757925, 729239969, 471699044, 842590967, 67836167, 802318742, 302043011, 916889522, 976405133, 455296174, 159758999}
167201298
261301421
271486625
500000
Returns: 2.107890254801774E-6
{306307448, 68886869, 378789435, 71477512, 255935683, 678139081, 880198463, 235341954, 248484279, 620848476, 371756169, 878980920, 750210514, 564246391, 641727867, 223079442, 966394874, 655287768, 482368042, 965327460, 368133736, 503462008, 685488435, 954815311, 943874553, 449905288, 429530089, 297934487, 674748994, 966684067, 31027824, 723734986, 6595258, 816536041, 872442858, 149239882, 411788345, 592468575, 110694460, 611581499, 251502525, 15317196, 262726751, 667911276, 78433488, 881107610, 643133334, 881430001, 445298673, 448205384, 873183444, 389658918, 422264446, 893760019, 750815820, 385202343, 234848451, 223289686, 84803970, 807341266, 319223186, 849781163, 33212038, 962171113, 449280555, 942996386, 817663474, 645210517, 181967208, 144108329, 117412548, 313781665, 580069100, 44258368, 454301039, 900480883, 670722727, 883124127, 552018801, 348857911, 919017868, 309996657, 985538650, 459605790, 474573564, 272234778, 441774254, 965787085, 241019610, 900374750, 701679582, 236188479, 798014240, 49392645, 936516822, 652728115, 425130917, 34802088, 971158046, 888496446}
434155183
41100150
49492551
500000
Returns: 2.1327691448022283E-6
{478607171, 588832951, 229422942, 749149649, 137416946, 107579939, 102452940, 674704014, 565576549, 634113707, 937003755, 755493201, 913294203, 375282662, 760290504, 778353646, 249827695, 273009172, 251402036, 870259150, 418910519, 945680758, 199781144, 617241919, 232862666, 182704895, 239126860, 972471315, 605464171, 726133577, 864875660, 339193677, 939353672, 629192226, 888881784, 428349662, 672063835, 67056700, 435783212, 420136281, 28064239, 21382416, 680197362, 600890997, 165601183, 108062384, 77164746, 698004672, 616672081, 647611985, 148533389, 393136796, 615173110, 362469585, 931383375, 395521792, 426667333, 443229772, 957910341, 922325372, 420967904, 902758464, 98947371, 603447089, 889395132, 730998662, 452699002, 316788630, 919176170, 492145113, 413030311, 726745180, 749214711, 153955059, 97813127, 634033597, 63134658, 287307568, 164558910, 422276628, 848729866, 95766755, 280165935, 66782640, 252083451, 126165173, 483855472, 13060977, 556563771, 75958828, 84184659, 677915, 462265509, 444809858, 361886899, 712241215, 642200316, 802027053, 73159176, 203373151}
704904332
529726882
827498484
500000
Returns: 2.1297077189126564E-6
{650906894, 403746295, 788884451, 423026514, 310070212, 533225540, 623469955, 819098806, 468808083, 647378937, 207284065, 923177486, 371345152, 305212400, 464992406, 38660575, 537055788, 894525848, 20436030, 480223572, 178515299, 96727498, 717869124, 283463790, 521850786, 34397970, 343690899, 647008136, 237416817, 485583088, 698723489, 655889843, 573349547, 441848410, 610353441, 826352909, 932339326, 541644832, 55839224, 642551799, 218486689, 441308372, 687602502, 828837985, 543940882, 36254633, 511196164, 924644814, 374184754, 138190582, 10022605, 105442670, 99253770, 241244621, 111950923, 405841242, 618486216, 368202590, 834811969, 37309471, 231540617, 951940501, 459649971, 244723065, 38337698, 519000937, 796562533, 398432213, 365213121, 545214629, 704852811, 258602154, 213327583, 263651749, 737529959, 662553578, 160579328, 986458284, 485927022, 786867349, 774646599, 291602324, 283621224, 260098763, 29593338, 983890839, 522141426, 470400348, 872107932, 952780389, 466689743, 60134618, 712656051, 836431807, 496084980, 357893580, 150441711, 274284744, 175160313, 932110599}
680686213
604492879
310537142
500000
Returns: 2.1071573814776654E-6
{19429265, 850286644, 400383269, 578300055, 559686685, 878565087, 615397643, 651289076, 648299603, 439367814, 167436063, 746214438, 539123083, 927275157, 225633882, 5314876, 87185261, 262869963, 177811369, 585725997, 200082436, 715546808, 636324894, 182945979, 306234324, 509236330, 660759478, 24053593, 490329798, 268486156, 916072132, 159005217, 132767728, 951628954, 908843524, 293847263, 63082660, 427229492, 412876153, 62931896, 967588505, 197888730, 66335062, 820989460, 798251723, 44278091, 890392152, 16504889, 315355928, 901956194, 274737890, 861985861, 698687127, 887626824, 203346052, 138769408, 364221705, 968083784, 518494768, 992604279, 133476406, 685151301, 281866828, 369107960, 566429146, 965384604, 821610828, 293875265, 268312444, 507191060, 32351969, 602635471, 327176985, 850716912, 676444054, 459127854, 25678922, 460298309, 798201391, 606354877, 240831122, 793362791, 921399386, 331629949, 813722608, 289929443, 711730822, 766939040, 823779588, 834806901, 149033714, 79679558, 171087122, 389052561, 231338885, 42282186, 694894338, 397530559, 698266644, 956994968}
624431916
758223114
526998741
500000
Returns: 2.060886840825344E-6
{191728988, 370232719, 956049515, 547144188, 441167947, 308005945, 841447390, 799479132, 260359134, 452633044, 732683649, 917693987, 997174039, 152172157, 344196519, 265621812, 665585357, 175558635, 946845370, 195690418, 955891959, 571626287, 150617604, 140339855, 300255176, 242035938, 470356250, 407418416, 126077708, 27935666, 749919961, 479496648, 65526135, 469317870, 339143178, 281785039, 323358151, 901817624, 324104169, 580314682, 452978216, 912781953, 483805673, 48936442, 176591415, 972470346, 615595567, 243145031, 781696604, 687502060, 550087842, 865463739, 182767787, 356336389, 88946339, 854121597, 851007856, 188023863, 96633864, 398760382, 944049127, 734333338, 642569428, 10383936, 711576455, 458419612, 456646356, 670486117, 5521399, 560260576, 33002465, 429459713, 496322596, 669241599, 316160879, 192680567, 123123592, 864481757, 410741500, 679773594, 170543119, 284165621, 924854674, 229978804, 591232494, 143859838, 750016776, 519245671, 139323741, 420456451, 531538798, 139136262, 130305659, 780674510, 365536966, 687934558, 203135733, 869788257, 509095777, 976904412}
895181065
538021843
305004668
500000
Returns: 2.1246985583920283E-6
{69061443, 181350799, 515511018, 224816318, 322649210, 733651545, 63701867, 238841185, 577451403, 465898275, 297931227, 794206267, 160257721, 963208435, 753931160, 820896016, 949018186, 502108043, 715879364, 391794112, 6668735, 13845031, 373738316, 511594465, 589243296, 388696280, 984985760, 786987976, 52997621, 787385183, 292595786, 91160075, 699522017, 576941322, 60614835, 265927551, 288666374, 671373017, 354225653, 93902197, 934572670, 623879906, 487415549, 981916169, 968791849, 904457859, 49626979, 469785173, 953070012, 591941393, 415372323, 282802345, 375676451, 526283430, 974546633, 864441046, 46621995, 407963949, 969740235, 923809959, 45793837, 492343371, 3272021, 651659918, 151691025, 660282622, 796714623, 43301698, 451558357, 908297360, 619792233, 256283956, 665468208, 483971021, 955877710, 516167817, 515535530, 563632466, 23281609, 753192311, 96459853, 774968458, 928309963, 423294927, 368742381, 706618236, 788302730, 271552303, 864933373, 301073269, 622871878, 608658436, 85728932, 762230988, 499735046, 452480391, 715172399, 637013215, 316129646, 609113}
457102211
26648568
788043333
500000
Returns: 2.0118052733439825E-6
{536328434, 701296881, 366144524, 898693190, 495302476, 454264407, 875890886, 678203245, 189510934, 479163505, 568211545, 965685816, 618308677, 188105434, 167461058, 376170213, 941279010, 414796715, 779880626, 1758534, 57445519, 164891777, 596859028, 879053811, 878231416, 830323890, 89549792, 461524797, 688745537, 841801962, 126443616, 706618774, 632280424, 94630239, 77053761, 958898066, 843909132, 145961142, 679314404, 611284982, 419962381, 43805854, 904886160, 209863151, 347131541, 127617369, 483658397, 286359844, 419410681, 377487258, 690722275, 581247491, 859757118, 994993002, 155114181, 870965232, 238440878, 332936767, 551674595, 38794058, 856366557, 836492676, 363974622, 292935894, 300633599, 153317629, 140578147, 714879817, 188767312, 256334137, 620442729, 83108198, 125785816, 593667712, 599389798, 249720530, 907947468, 967815914, 344649721, 412750293, 317343854, 265771288, 517904516, 616611050, 732391540, 560548631, 830383947, 318826202, 180477527, 472862091, 300344223, 668115140, 41152205, 157648194, 633933126, 98132756, 223413794, 695410177, 831991518, 20518558}
432884092
101414565
566049259
500000
Returns: 2.033140185015757E-6
{413660889, 221242957, 921810770, 867537324, 376783739, 588738004, 806973365, 117565298, 801570471, 492428735, 133459123, 547230829, 76359626, 704174444, 282228431, 931444418, 519679100, 741346122, 548914621, 197862228, 817050305, 315938524, 406119006, 836447686, 872252268, 268156229, 899146570, 844889621, 324493447, 601251472, 255258713, 23314933, 270071563, 907286430, 798525426, 943040578, 809217355, 620549274, 4403149, 833700500, 491491363, 758699078, 617324031, 437810139, 434299235, 350776885, 212657077, 512999986, 590784089, 576893859, 261039487, 289758101, 52665774, 164940035, 40714468, 881284681, 430259761, 552876853, 719748227, 444950169, 371972003, 594502710, 429709954, 930416613, 445780908, 646352644, 775613682, 91490662, 634804270, 604370921, 916060493, 496071712, 999964166, 703364403, 534073891, 278240511, 300359400, 371999355, 662222569, 486169009, 243260588, 51541386, 521359804, 514959905, 214934159, 709446294, 868669901, 776165573, 496021687, 353478908, 682849307, 727571843, 996575485, 844237411, 768131206, 743785128, 440483193, 167667867, 933992655, 44223266}
703633241
881213301
344055185
500000
Returns: 2.1632426141489047E-6
{290993344, 36156300, 186305004, 836381458, 549437005, 14383598, 324195109, 556927358, 118662734, 505693965, 403739441, 9882374, 239443314, 929071451, 986930340, 195546611, 806907192, 949002062, 612915883, 807826656, 572859821, 463190007, 629239718, 498874293, 575101116, 709783840, 708743341, 519426442, 251413360, 360700982, 797934545, 343806363, 202829970, 424975346, 818759616, 222150352, 69492839, 390104667, 34524632, 642255283, 681913813, 469797030, 329761903, 370789860, 521466930, 573936402, 351721227, 739640128, 348296762, 67472457, 126323968, 707096713, 950607176, 633649608, 926314762, 891604130, 917045912, 772816939, 301682587, 264967007, 473716720, 643684747, 790412554, 866659857, 885895485, 848215654, 410649209, 468101514, 372013225, 657440437, 207882985, 27928687, 169109770, 226921822, 173790715, 11793224, 397804070, 362322068, 274762679, 850759730, 172972585, 956204959, 819782361, 708276028, 992444053, 977237424, 611988587, 528472204, 811565848, 234095726, 65354384, 492061279, 955794023, 530826621, 193501283, 508330960, 657552591, 639925565, 744821788, 64132710}
970587127
366044763
122061111
500000
Returns: 2.067863132275001E-6
{463293067, 556102382, 36938511, 805225591, 725885536, 734996467, 550244857, 996289418, 730722271, 518959196, 263954288, 886394662, 697494271, 740107722, 810525709, 750820815, 385307282, 275551463, 381949877, 712758346, 623636604, 614236754, 852360430, 456268169, 864089236, 856444182, 522135376, 193963263, 182128538, 411322497, 631782374, 250437059, 426760381, 237631531, 540231274, 620153599, 329768330, 569725530, 654580652, 159638061, 458475528, 184690247, 38404511, 598736848, 899806629, 502128650, 80719907, 261247531, 519670170, 266879058, 692845924, 5541852, 729655104, 803596648, 106882310, 606956312, 108864788, 992757025, 879821690, 379951113, 284289433, 987834052, 856147886, 212968565, 326010055, 636217929, 750717476, 844712365, 109222180, 714305217, 503500749, 149720197, 338255381, 336618512, 108474807, 40313206, 204076736, 61472777, 596130791, 219145708, 803922058, 447007789, 118204910, 610420146, 356093205, 126135080, 359102537, 280778836, 127110001, 114712544, 742826735, 965378717, 911217296, 217415831, 327699363, 153983326, 165793986, 702117791, 551855657, 792870157}
946369008
145843492
900067044
500000
Returns: 2.1216152281054614E-6
{635592790, 781081197, 596400021, 187930453, 607366799, 869470064, 67466601, 140684203, 342781802, 532224426, 120373870, 57874204, 446717224, 965004728, 515227611, 11127744, 377568106, 893272874, 445951139, 613894772, 383241384, 60250761, 780513874, 827522779, 153077349, 589243789, 331732148, 282360819, 109048451, 170772007, 170662935, 570928489, 769584260, 755320454, 261702931, 899263379, 298871816, 44313655, 979669403, 382053579, 943865246, 895788206, 750842390, 535511833, 986974323, 434116163, 219784057, 782854941, 691043578, 757457662, 263163137, 714052469, 627596500, 977338952, 992482604, 617275761, 300683671, 917729843, 47895315, 786107223, 386034150, 450876817, 216850479, 559277279, 179985360, 424220205, 94581000, 221323210, 260291870, 62341994, 504151245, 681577178, 212433724, 446315203, 751986903, 68833187, 891455942, 465656225, 208670900, 292564425, 24806053, 232777887, 416627467, 508769001, 133603092, 980065482, 692355759, 33085467, 151482158, 700362100, 125331812, 729868153, 571673301, 904005048, 461897444, 213496426, 382863384, 174375481, 653856794, 812779602}
217118150
634470224
383105702
500000
Returns: 2.0528401042842772E-6
{807892513, 887166544, 447033527, 156774587, 780020065, 148389, 998549087, 875013531, 659874071, 545489656, 390654188, 934386491, 904768180, 776040999, 338822980, 566401948, 661000934, 514789542, 214985133, 223859194, 434018167, 502469512, 294806584, 784916654, 147098201, 30871392, 141328919, 251864908, 449829099, 225188785, 713338767, 887624656, 702342667, 567976638, 986969860, 592233887, 264180039, 522697051, 9790880, 190608362, 425459692, 610681423, 463280262, 468491553, 74142011, 362308411, 948782744, 9495076, 157384247, 956864263, 538513088, 426358343, 111677160, 151081250, 173050152, 332627942, 496297817, 137669922, 629829682, 606124061, 901639603, 795026122, 577553079, 495520523, 620099938, 917255219, 729616535, 597934062, 997500831, 410378778, 90941006, 803368689, 672751339, 261044626, 686670995, 802385907, 988900612, 164806934, 821211016, 657155146, 659550789, 428613456, 125115487, 997052392, 911112986, 542823873, 730641713, 80359367, 172059051, 872150922, 802804164, 789324856, 530891838, 590594258, 596095524, 564181530, 891104787, 646633179, 464685927, 832689046}
779039303
709236221
161111628
500000
Returns: 2.090873546058808E-6
{685224968, 407112619, 711527769, 830651459, 661501328, 720761258, 810738100, 19408316, 268138337, 558754887, 955901773, 102070769, 362819129, 937998, 43524883, 121676145, 948229027, 132510946, 984019134, 128790883, 484794951, 653516259, 517927296, 447343261, 436086321, 472499003, 245892958, 635229732, 671716281, 984638302, 842153864, 503083347, 631305810, 85665555, 3408779, 576376399, 819422798, 997285183, 334879632, 413023879, 205816671, 30607371, 171922870, 696438541, 452481710, 585467928, 87846887, 531102486, 619929659, 742410129, 403797569, 429836221, 304585823, 321028290, 54855175, 342947392, 688116700, 357610008, 502936046, 721108168, 3384313, 258068887, 643288412, 841829238, 60214508, 119118222, 69684795, 974544913, 443537782, 463448294, 91591502, 630192931, 136864211, 79569312, 326387820, 125873149, 381312543, 568990382, 847611860, 730573863, 880434791, 628244289, 423538043, 895401247, 979794877, 396754267, 477755662, 537698737, 487603211, 752767740, 185309241, 258847024, 486315112, 277183468, 730293604, 918661898, 108174178, 118890869, 566687064, 856393754}
754821184
489034950
939117561
500000
Returns: 2.179983824520022E-6
{123456 }
234567890
345678
456789
500000
Returns: 2.242434027590908E-6
{123456 }
234567890
345678
456789
499999
Returns: 2.242434027590908E-6
{ }
53453
5654
534534
500000
Returns: 2.063736436092274E-6
{ }
23525
46426
134
500000
Returns: 2.1314599221590837E-6
{1 }
13
228
322
500000
Returns: 2.0553041233511323E-6
{ }
1
1
1
5
Returns: 1.0
{2, 5, 7, 1, 7657 }
345
657
879
500000
Returns: 2.1021563920269413E-6
{ }
234567890
345678
456789
500000
Returns: 2.242434027590908E-6
{3, 3 }
3
3
3
2
Returns: 0.0
{0 }
1
1231323
456
500000
Returns: 2.097337430132447E-6
{ }
11232
11221
11213
500000
Returns: 2.094464539668111E-6
{5665, 465413 }
151561
452452
74522
500000
Returns: 2.15644583223714E-6
{ }
325
3253
5436
500000
Returns: 2.1932325616079027E-6
{5 }
7
9
24
500000
Returns: 2.125213318286823E-6
{12345, 23456, 1111, 11111 }
1000000000
12345
23456
500000
Returns: 2.0925580266340784E-6
{3 }
6
7
9
500000
Returns: 2.0286526906020637E-6
{2, 0, 1 }
234
234
234
3
Returns: 0.5
{ }
234
135
245
500000
Returns: 2.1978505022088398E-6
{ }
232
235
143
500000
Returns: 2.110479374285075E-6
{ }
89635448
1
1
499999
Returns: 1.0
{0 }
1
123
456
500000
Returns: 2.052713687494868E-6
{ }
506956987
633866516
928388084
500000
Returns: 2.130996624501347E-6
{ }
666
999999929
41
500000
Returns: 2.1100963892030586E-6
{ }
12
1
1
500000
Returns: 1.0