TopCoder Statistics - Problem Statement

Problem Statement

Bearland consists of N cities, numbered 1 through N. Some pairs of cities are connected by one-way roads of unit length. The distance from city X to city Y is the smallest number of roads you need to traverse in order to get from X to Y.

The road network has a special structure. You are given a description of this structure: two int[]s a and b, each with M elements. For each pair of distinct cities (X,Y), there is a one-way road from X to Y if and only if there is at least one index i such that X is divisible by a[i] and Y is divisible by b[i].

For example, suppose that N = 7, M = 1, a[0] = 2, and b[0] = 3. In this case the country has 7 cities and it contains the following one-way roads: 2 -> 3, 2 -> 6, 4 -> 3, 4 -> 6, 6 -> 3, and 6 -> 6.

You are given the int N. You are also given two ints S and T: the source city where you start your journey and the target city you want to reach. Finally, you are given the int[]s a and b described above.

If there is no path from S to T, return -1. Otherwise, compute and return the distance from S to T.

Definition

Class:: FromToDivisible
Method:: shortest
Parameters:: int, int, int, int[], int[]
Returns:: int
Method signature:: int shortest(int N, int S, int T, int[] a, int[] b)
(be sure your method is public)

Constraints

N will be between 2 and 10^9, inclusive.
S and T will each be between 1 and N, inclusive.
S and T will be different.
M will be between 1 and 1000, inclusive.
a and b will each contain exactly M elements.
Each element in a and in b will be between 1 and N, inclusive.
The pairs (a[i],b[i]) are all distinct.

Examples

11

9

6

{3,10}

{5,2}

Returns: 2

The one-way roads are: (3,5), (3,10), (6,5), (6,10), (9,5), (9,10), (10,2), (10,4), (10,6), (10,8). The shortest path from city 9 to city 6 is 9 -> 10 -> 6. It uses two roads, so the length is 2.
123456789

18

12

{1,42,50}

{1,17,3}

Returns: 1

Since a[0] = b[0] = 1, there is a one-way road from any city to any other city. In particular, there is a road from city 18 to city 12.
60

30

8

{16,15,12}

{2,20,5}

Returns: -1
77

10

62

{2,5,7,4,17,26}

{25,7,11,13,31,34}

Returns: 4

One shortest path is 10 -> 56 -> 26 -> 34 -> 62.
100

90

40

{20,30,100,99,100}

{10,30,100,100,99}

Returns: 2

The only optimal path is 90 -> 60 -> 40.
1000000000

7000

424212345

{35000000,120000000,424212345,200000000,3500,19}

{15,1,7000,200000000,400000000,17}

Returns: 3
2

1

2

{2}

{1}

Returns: -1
1000000000

221699492

869825265

{906660545,914071332,546674226,65436974,36486149,541052406,74684889,846035224,714756927,70561759,569874292,592953677,718101400,887495882,30141044,449916121,13730386,694259170,824307829,6918727,69523629,439518988,64297856,62701634,717988662,939079403,571549186,439518988,864330042,509570973,846296315,39037046,367927383,530406650,464896663,367927383,37972588,718101400,362730712,569874292,756861067,401675068,64148788,61457693,1853091,456291950,437683803,780926758,402151583,790392502,569874292,509570973,774229806,756861067,887495882,31008221,59813555,24430873,439518988,938070375,906660545,815206147,55240555,780926758,10564143,482726064,846296315,335892162,402151583,939079403,439518988,50597680,335892162,5845109,21644,467239961,45844853,402151583,4740950,379362613,530406650,26535733,43836875,714756927,947203968,927862863,938070375,464631653,30873575,717988662,456291950,343659772,824879753,592953677,914071332,335892162,63813832,52930780,23819381,33262379,464896663,467239961,834168160,21644,864330042,846035224,401675068,718101400,34054864,741279325,694259170,774229806,356979952,568832871,569874292,44106987,50958426,546674226,996976128,482726064,31173818,790392502,362730712,15222085,571549186,44561943,824879753,815206147,32740421,996976128,530406650,456291950,464896663,12874433,780926758,6026077,482726064,914071332,568832871,694259170,449916121,899371520,996976128,714756927,33829152,834168160,887495882,938070375,906660545,66682213,718101400,815206147,35555112,69696763,437683803,993743446,996976128,32675805,8000944,55527912,50697748,20516577,927862863,367927383,10696452}

{64423968,9821551,938070375,780926758,571549186,569874292,927862863,864330042,65718887,824307829,33311470,864330042,18649526,335892162,887495882,694259170,824879753,78460429,914071332,717988662,694259170,82690294,717988662,568832871,18549127,509570973,335892162,31328554,467239961,68128813,343659772,780926758,993743446,482726064,717988662,2863264,467239961,21380465,482726064,13467004,846296315,939079403,993743446,906660545,509570973,546674226,26007730,4017496,439518988,53348843,28002264,774229806,906660545,53161556,834168160,815206147,509570973,756861067,464896663,824307829,63221441,846035224,887495882,24045528,401675068,43814313,32776003,362730712,12220929,906660545,717988662,846035224,81467516,439518988,41205621,14193208,714756927,464896663,509570973,437683803,68936705,541052406,362730712,34837095,899371520,541052406,914071332,456291950,717988662,815206147,824879753,947203968,938070375,996976128,887495882,2181153,694259170,541052406,482726064,927862863,57424961,464631653,571549186,379362613,456291950,22764969,71493526,541052406,464631653,449916121,790392502,26901586,568832871,6393307,401675068,993743446,482726064,824879753,32063753,780926758,592953677,714756927,530406650,717988662,19905715,571549186,83165308,592953677,464631653,846035224,39864709,53217989,815206147,509570973,356979952,947203968,46229781,36124900,756861067,7860274,714756927,258185,17300595,718101400,947203968,64948714,67993575,20986054,402151583,947203968,927862863,60265451,335892162,439518988,367927383,741279325,34066792,569874292,356979952,401675068,568832871,464631653,55443020,58252076,356979952}

Returns: 35
1000000000

296636375

286500240

{731942452,374532828,850605016,507945735,577278873,499077959,520391929,758903563,784079413,991076737,617524021,882280735,713169548,850862334,575226829,433292170,710382832,29583837,971189317,39258965,865036751,784040271,409467310,654775914,442350634,409467310,989219208,382881705,670005237,8475325,868909172,368030411,793225907,364040593,621290118,515109072,894723859,875853316,686615156,768730337,764968326,415546549,801338329,890747896,39523948,793803609,621418494,404876067,495890537,510085252,704330550,963631953,341904967,844880143,664916136,515331638,447000263,899367603,825728862,337688429,745046880,851873916,488914623,792636341,341904967,662184608,360305326,647280415,817756563,440013751,537207083,862112762,781685120,843573473,370345492,726318931,959387185,562199388,663335257,667388816,815398414,667081870,732218196,676605676,568736606,20308235,411281003,345024645,418640709,959387185,871099530,82223,867740719,372385659,913953223,410347861,388694793,590434525,444546211,914602305,349015703,686855081,354588785,736527283,568545360,648056810,690710043,995766587,369407336,382461161,493073608,522915545,847658344,656879304,797593972,568905192,961078578,590176149,624676762,452249306,522915545,884612264,736802488,954974350,710547986,333581442,511616386,868909172,653726763,984981113,924107145,713199585,473987370,907771103,756113167,368030411,793747278,647195225,773685446,772383138,568736606,985234782,566505637,542969159,712428155,664710319,731518756,515466594,534035295,627089970,761020126,14695863,958057834,562199388,617524021,801338329,994954507,984672960,649142224,865058502,949294876,594974327,364693914,579875587,28072485,815380511,772383138,714194828,970825120,740628344,396281729,590985018,54289596,696795650,1298738,345362275,762151057,429469928,493073608,909438240,384051702,679368764,426977614,965225646,601360889,510085252,952396092,386802614,632420563,850605016,64594112,531623551,655066060,949294876,713199585,586387407,542559353,424794570,64628122,858664361,396281729,610194697,919240243,820430844,907771103,716541020,434199235,864492387,359199328,762151057,635567182,580085492,574344603,752915577,792627183,900674560,997297988,793097132,969234200,388694793,907771103,373475497,943133499,361293508,634100830,552674053,485621818,537207083,414545806,474532972,48219977,634069451,65265456,980080047,893123594,765304722,889177038,8475325,46844826,745046880,499077959,447777292,756102938,461785139,704330550,631641558,520472791,868909172,896016728,39761464,399673965,798951370,25800336,364693914,969181459,45608250,439036191,943133499,710547986,736802488,913974509,988912956,11375437,768102424,858973213,399089983,820430844,777573660,739334161,631641558,516138437,713169548,680025219,577278873,643034064,925144096,930169228,972047587,23008146,461541577,352225476,636100464,522679968,898812160,622335281,480136844,350589570,775039972,568039078,867227886,342259974,955701817,677747895,65573187,794975488,621508839,812564717,360346320,495890537,900674560,412208382,924757362,375955548,882706232,730859713,479001748,910374913,579770556,647280415,882541974,494768031,632420563,955022109,889177038,503482032,590176149,447760214,410347861,965780622,938451648,646993025,454390842,342750849,500716291,25946816,955701817,49596352,35586359,351486946,360346320,568039078,625015576,781685120,4048157,374561911,439534733,360955358,384731344,590434525,604706711,603501651,555593443,980667789,679368764,38490341,547104803,731937225,590101133,76526832,568736606,492624832,931266323,867740719,984981113,913953223,902228934,461785139,375955548,941921502,776494290,582542040,360305326,808773332,361127335,382497243,580085492,522055237,845903538,499854432,664710319,909438240,47674163,29812452,915852177,710382832,384051702,881374603,783871090,653806474,380011449,881374603,928731959,342750849,29382982,407782836,548096077,637612951,421370203,775039972,815398414,501194122,500615310,46654960,66657418,906814483,591247287,852667212,360955358,950900637,64555074,594974327,518783954,488777702,671727911,552674053,566505637,369649856,577146114,480136844,843508354,691528135,434199235,12157663,850605016,830873900,606534115,954107791,830873900,879764632,466135149,429469928,380011449,369649856,361293508,455649107,394023478,590434525,752800938,788040945,810884719,934551902,807891535,544116140,569244831,388571102,621508839,333581442,862112762,487054159,928324065,349015703,590733483,642633099,607109149,720288694,775209808,542969159,657983540,798951370,6247425,505335544,840661225,924594965,412208382,351486946,775209808,426977614,768730337,713199585,575821959,1330297,777573660,772358400,818439272,563385717,53653117,658321132,388571102,642598861,962917369,519392193,764630818,951763230,924299685,983618448,631641558,752183551,729819924,7836639,361127335,938451648,860481339,970825120,911421873,419991363,861673721,427377318,784605581,374561911,865058502,938451648,380011449,566505637,628441065,678702503,851873916,362986933,735841345,648056810,368030411,976127228,765898511,44792224,959641493,711414106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Returns: 90
1000000000

932271153

645801325

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Returns: 72
1000000000

818638264

620642160

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Returns: 34
1000000000

923185852

255706569

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50695580,656261023,609215437,503590483,959700823,574369787,618929309,710788407,461527276,364690890,653826921,601355538,867127391,791630254,841542806,568055172,853178815,719426512,339651554,559294251,2704372,499187982,667694574,668121287,701312193,683702810,582924317,494199318,630149605,2776844,479458661,557227657,854172554,433361728,775413547,970542898,688372993,761332872,870950000,519261264,460957,939639627,723374633,787854090,964684712,902420044,370407821,527323064,554125617,568055172,579885608,978411945,219993,775555811,483025318,709959061,872983717,961253660,734750942,707140702,657049107,812530923,405630460,980818440,757156008,633068340,975773110,370407821,635577013,508261209,978411945,875363948,335321117,655259712,687930472,551650360,678669439,822462577,783225507,646645959,937210979,336480757,545420708,349953817,860332005,877130575,346359310,638229752,984518828,497607138,602393933,865988545,336352198,802903045,475970616,359697372,473393383,743048310,334702457,942831497,952109609,397620975,893169785,870522013,985612571,808436389,859652532,466888447,694257404,2848418,542720986,2596334,653826921,766987745,582827204,564287966,653175125,463394733,593422275,506360266,914612574,976890733,582308200,787645641,981887061,454446773,702968302,617184364,686918907,646637578,999152587,834459401,877884563,461527276,2494608,500908613,497607138,813662235,846981813,905771286,383713122,429780152,761067036,477267382,698288426,769393392,336352198,557390399,720974842,1940420,949889612,466888447,976890733,583473189,697239149,474657511,595633487,635483804,534116097,574369787,813210884,865988545,860332005,667694574,551870418,455584727,425981345,674082771,438308321,609215437,738587231,372772319,659738010,617184364,361878461,589389099,1583544,656261023,991562087,864845767,362220979,927136063,520751735,538312,880182920,803512355,426270453,533109316,718490818,458548373,999152587,384333651,368836372,336480757,2961744,848420918,533109316,858750695,4576402,428886286,441836771,526134363,675525898,664803167,559248579,1368888,655259712,937210979,635483804,688372993,428886286,815312938,456596215,397068591,463394733,373402508,3747702,939639627,793771,914612574,402256602,682131796,859652532,858750695,346194041,970542898,607850515,645791300,694167664,809562028,963271773,973035056,838865867,369012959,630149605,357085231,950695580,375988749,645360835,673467982,815294761,343209715,497607138,567342027,2650421,751170214,490168547,1354335,499187982,456596215,690553000,628152235,844880068,459114094,995632973,905771286,991562087,808436389,1460549,670151626,513620260,702968302,663440496,341925960,635483804,843183122,746567760,582827204,935690072,684114067,746793067,701815742,333896608,870950000,339309019}

Returns: 330
1000000000

759778786

852355230

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Returns: 12
1000000000

974102984

734829480

{30,57,27,398643387,83,23,23,95,73,84,47,2,44,96,552326069,4,24,30,492244271,31,65,37,10,38,47,91,793394438,68,694671312,64,40,70,25,53,100,528021365,38,76,7,13,95,78,98,39,100,12,627584415,90,975190375,12,70,98,56,37,877518965,781203195,76,81,59,90,621568543,535128606,35,49,52,25,38,97,2,31,14,44,2,77,36,495548192,33,79,39,97,89,67,434545268,60,75,920291194,62,826894087,602979495,26,81,763161890,676250369,81,60,34,88,33,18,88,61,58,832373464,79,573156091,754549737,26,32,69,402601413,550434900,22,91,78,32,72,78,67,21,353395616,913224979,34,426496541,99,74,592012703,27,45,81,31,21,100,74,29,13,66,100,11,31,38,826894087,33,76,737449735,98,54,22,86,55,8,7,403264034,41,99,55,694671312,70,41,20,587235657,591672346,55,38,37,963848386,1458238,73,53,52,62,11,17,61,37,621568543,36,20,35,44,398039590,56,70,421745727,55,97,93,10,13,91,9,573156091,636935121,7,57,8,13,372183355,74,96,640665790,509912085,75,763749579,82,50,981470181,60,54,9,24,72,48,70,31,32,100,90,753946430,41,13,39,24,54,7,48,8,877518965,6,18,35,401838170,99,92,60,65,24,83,64,100,627584415,28,79,9,21,640665790,943790016,55,758383899,100,28,75,34,91,421745727,27,963848386,4,41,83,83,26,70,32,75,50,44,68,764024532,60,45,69,532311170,26,46,65,56,75,2,789413055,72,8,46,97,27,93,885836644,588788383,51,88,38,6,692198863,63,71,68,93,417797021,755382895,78,90,54,4,38,93,588788383,33,86,969311565,8,649703405,54,17,83,398039590,932387102,31,76,415983442,11,835510963,96,76,749014814,2,80,47,59,763749579,61,20,74,67,16,398643387,90,82,37,45,456522072,60,608591620,345726612,587235657,89,58,39,85,399194989,87,978310271,467089567,82,72,753336205,29,905551256,775073464,37,92,100,63,54,728272536,63,63,68,14,56,52,383713178,979346854,45,38,936165856,60,872716190,503528482,21,392879324,3,30,2,81,85,38,60,72,7,350306363,11,770698989,429233366,9,82,66,3,1458238,37,57,66,693456833,88,48,61,3,58,84,906753059,17,528021365,66,69,38,86,79,65,53,13,14,48,660331909,53,83,98,40,44,46,33,399507598,14,92,97,14,63,69,905551256,69,67,56,92,2,47,10,30,982217808,52,15,368619154,847852312,69,9,447685535,99,833469569,11,774906705,14,418476385,793394438,80,7,9,467089567,621168323,832373464,71,588788383,61,92,100,83,14,64,880998054,758383899,87,737449735,91,98,13,71,422030739,66,11,37,66,393453051,42,88,37,70,57,39,49,936165856,36,77,68,22,1,85,452994019,47,79,42,70,56,9,858175118,43,604632088,17,9,76,970053766,741288863,725985482,912327533,79,11,52,56,75,27,604632088}

{4,71,100,350306363,39,36,89,44,80,79,98,59,87,68,587235657,63,17,17,383713178,60,53,86,67,42,13,13,621168323,54,636935121,27,29,49,12,12,34,913224979,65,80,4,18,93,67,99,80,83,56,749014814,74,764024532,30,31,4,40,58,975190375,763161890,11,62,94,66,877518965,905551256,86,90,81,17,83,7,74,90,28,30,53,71,50,753946430,12,53,23,80,93,32,693456833,27,89,781203195,77,692198863,763749579,38,56,981470181,872716190,9,55,60,9,61,33,51,29,54,509912085,25,694671312,640665790,11,82,46,979346854,602979495,51,97,52,20,99,44,64,95,495548192,789413055,37,368619154,24,26,452994019,39,27,45,19,68,35,77,76,67,56,39,70,99,41,418476385,16,45,694671312,77,95,67,18,56,95,26,550434900,22,54,72,402601413,96,49,39,978310271,415983442,64,73,29,372183355,755382895,85,16,20,20,89,57,28,85,421745727,3,76,6,48,932387102,1,94,877518965,89,78,21,7,33,75,54,737449735,858175118,43,95,71,42,591672346,47,49,975190375,936165856,1,421745727,46,97,447685535,18,32,5,47,32,91,80,25,47,80,47,528021365,48,46,97,22,33,37,71,15,754549737,99,50,31,456522072,41,62,37,42,33,48,20,81,426496541,68,72,46,50,970053766,401838170,32,503528482,13,30,31,79,8,640665790,2,753336205,12,18,46,85,84,63,15,100,53,1,37,970053766,62,51,10,835510963,25,18,16,86,16,8,832373464,82,39,63,5,70,3,694671312,393453051,30,50,1,45,660331909,65,24,42,60,826894087,676250369,6,12,71,99,63,17,422030739,24,1,833469569,48,758383899,78,10,13,532311170,532311170,48,86,573156091,66,399194989,42,16,774906705,99,89,44,16,725985482,12,93,27,98,24,399507598,59,22,68,67,920291194,100,422030739,503528482,906753059,55,67,26,31,793394438,69,943790016,963848386,87,74,372183355,24,627584415,649703405,77,54,99,8,97,552326069,16,24,95,21,57,67,398039590,636935121,1,92,775073464,51,467089567,398643387,58,2385810,34,30,4,97,55,95,34,29,49,847852312,56,417797021,392879324,37,33,99,39,676250369,84,39,66,429233366,11,75,30,98,20,14,978310271,87,832373464,63,98,54,11,49,81,27,99,72,10,418476385,41,28,65,31,2,56,67,604632088,31,47,60,98,86,7,774906705,24,34,35,66,34,14,86,10,775073464,42,91,741288863,880998054,34,44,434545268,46,403264034,63,426496541,19,492244271,495548192,88,12,47,912327533,353395616,936165856,22,608591620,41,98,82,90,85,35,535128606,345726612,38,885836644,53,5,20,3,393453051,92,93,26,53,728272536,56,48,92,29,47,14,68,982217808,97,33,77,64,42,32,588788383,99,65,85,58,32,27,969311565,82,847852312,60,28,82,770698989,592012703,621568543,963848386,38,28,59,99,4,85,350306363}

Returns: 1
15123123

5680852

14818375

{9563,9943,3289,8146,5648,4877,2553,5947,3384,7191,9924,5321,3552,1316,459,7800732,3538,5752,8724,1577,4902,4668,3414,7304405,191,9025,7582,9876,7647,6633,5866,8264,3377,4140,8193,11250729,574,8499,6157,11574291,10173465,10114967,3443,4776,9059,6889,5178,4876,9532,2634,4277,870,5331541,9117,3408,8284,13649239,7775,5582089,1714,2916,14858890,2204,9705,7614,11176114,980,6001,727,14000845,3817,7997,10049,5372,5067,11574291,4022,9015,7345,5154,3083,3539,5101,3170,10361579,8457,2079,9371,2541,8380,8660,1281,7887,5374,1152,2765,5809,9951,7242434,7913,5529,6295,496,6813,4132,1941,9483,10708695,8785802,639,2887,5246,5758,5507,8992,8399,1038,6561,3821,7331,52,9978,9681,7213926,2986,4933,1198,7710,6212,2642,630,4922,7303,826,5208,9992,8056,7712,8528,3536,5980,7168,6315,1096,4449,7042806,874,15025927,7172605,880,4404,2198,8785,3894,7928,12813622,6648,948,6678,8261,474,3340,5671,2826,6818,7115756,8550,9127,7989,11256565,10114967,6572611,8525,4360,2689,3767,3994,9409,5975,6101,4948,925,950,7047,7246233,7687,3389,2000,10074,7488,1232,5728,5331541,8706924,6471,5455,3176,8626,7412,9639,2044,80012,1628,9708,9163,7631,5271,483,3656,227,13434456,768,9526,5965,5323,6662,6158,7423,8938,9598,5511622,396,3526,9512,4891,6645,7705,7946,5913,86,5820,5722,4291,4171,6993,3778,9541,10079,8154,8290,3131,3071,9804,1785,3170,3125,981,6104,2213,8867,9501,7042806,7366,8107,5928,2951,3863,8087,9850,5509,8343,6301,1706,5271,6585,414,9613,7210,1151,1650,8530,9525,7934,2948,9893,2470,2118,3562,3027,7737,9925,4947,3969,2771,3844,5236,459,1338,4760,9510,879,1374,2369,12774470,313,8456,9263,1807,5562,4762,9582,8689,6728,9063,9856,8095,10101364,1615,9313,2727,5903,6367,10052,75,1111,10997788,7688,5752,115,6577,3451,8141,7277853,6572611,7062,7753,13037296,10708695,6134,7138,3254,1460,6480,6908,2251,8001,2569,5306,1831,1146,6767,3317,7394,3236,8245,3184,4819,9888,8163,2740,7451,12322601,4643,9562,3856,9101,10361579,3949,6403,3423,7043509,7425,3398,14944055,4304,1006,9529586,3392,3138,2702,5989,9084124,2295,5850,2685,157,5838,11066613,2261,58,8706924,4,5231,1522,7974,8541,246,9084124,7442,6728,9500,8224,8708,4554,6763,7056,4809,9744,2686,717,874,2088,2435,6659,8070,2961,6337,6266,2516,4381,8498,5556,6541,4390,9183,492,9176,8469,2489,6184,6295,7544,8623,14025073,9479,6734,9304,9843,3757,5990,5859,925,854,12058797,5547,7502851,6495,5511622,358,12461685,4182,12774470,3948,6588,9197679,6502479,7758,8291,4910,4040,3611,14765738,1547,6923,12176164,152,8617,12924654,6052301,7405488,2403,1388}

{1871,4214,1853,628,121,3913,8654,1448,2994,9461,9941,2390,4536,8878,5996,12461685,9033,1182,8292,4711,5116,3300,9778,12924654,399,1528,8662,7983,5465,3887,1011,7793,569,176,3818,7405488,960,7081,2099,11256565,7242434,11250729,8589,5671,3462,6731,840,1894,6701,3444,9136,165,11256565,6745,8799,7738,6572611,5981,7213926,9015,2069,12774470,6760,5599,6988,5331541,7380,8365,2612,11250729,1108,609,7236,7605,1606,7304405,4168,5664,1382,8533,5328,2636,6797,9020,5331541,975,621,9733,4212,1879,1436,2564,9156,2589,6246,3566,5325,1122,12058797,5088,3072,6154,8062,5171,5697,9912,5268,13037296,14765738,266,1151,3632,5747,2961,3550,4911,2694,5635,1685,6095,40,5554,7281,7043509,8701,973,9057,9660,7532,6809,5948,6165,6827,5736,2764,1487,4014,7619,2508,6086,9300,7539,2076,1180,6781,7172605,8782,9529586,14025073,8648,2649,7465,6713,9806,9672,7115756,616,2359,5684,1743,3745,484,394,8154,1063,10114967,9752,9897,3400,11066613,14000845,7242434,1933,3188,2695,9865,6333,3369,1305,3961,7345,7800,9316,6953,14944055,5773,4582,7191,1867,10036,8332,1088,5511622,10101364,4122,4791,8865,5721,8197,9720,4737,10997788,1872,6641,5243,3897,465,6813,8611,4660,15025927,7753,247,3115,5921,4614,7503,5218,3210,1900,11574291,7754,3447,5461,5007,8015,8594,6172,7692,6763,8697,9613,5637,5772,3590,3742,6790,5289,123,5190,7543,7201,7272,5456,575,2942,10,3405,1974,7173,3785,12176164,153,2166,6006,1561,4586,7967,146,2821,8590,964,1836,7944,5058,7034,2108,796,7949,7943,4517,1303,1848,9392,2074,2837,7902,1361,798,4228,9669,8008,9922,6532,4817,6455,1264,9950,5546,7617,1590,4571,1622,5582089,269,6302,2678,2864,266,6477,2583,7408,737,2535,4884,9260,12813622,4451,6230,7120,4189,4476,7961,2597,1800,7502851,5846,9726,4078,1895,5973,8439,13649239,10173465,3043,71,13434456,13434456,3687,6033,5747,2961,4414,3880,8809,8812,9205,1281,9484,7253,3737,5825,9660,909,2235,4052,2617,2348,8589,7130,1253,7800732,6214,1839,7810,5093,11176114,9684,6526,6640,8785802,4148,8871,10708695,710,5875,14858890,10057,1083,2853,902,10101364,6895,5359,2465,1107,8760,7304405,5190,2844,9084124,2011,4067,3818,8773,6853,9501,12813622,1912,9058,1586,5083,7390,5817,8841,6962,8308,3344,9932,6813,4842,4689,1105,3450,1607,7739,9847,1850,3783,2327,9745,5031,6244,1053,736,5967,8100,5922,3834,2694,8865,3083,4193,6052301,1816,5703,1855,3005,6168,7091,7021,2474,6117,12322601,1755,8706924,1747,11256565,420,53885,3241,7213926,4215,782,7246233,10361579,8060,6139,2052,7595,6094,7042806,1978,8291,7172605,2117,4449,7277853,6502479,9197679,877,6169}

Returns: 7
1000000000

749769804

334865945

{533611788,533611788,823436946,685011884,832190652,949728057,4671019,758151,369281587,966260208,5631653,15605438,393658973,791481283,760212824,378070839,19432314,626392058,5446178,472227679,20674466,608713133,5812468,944155252,3605918,1028339,412303403,791481283,823455219,802140376,472227679,5468130,21644,892449850,3842257,549214725,832190652,455436630,12325724,14131954,5596933,484586129,861729319,626392058,5925867,22687098,960068421,787284682,10578378,496737560,478214565,626392058,940535029,994370566,416518755,414854327,414854327,710076313,19762383,752922786,710076313,396940379,3091235,357144797,901595351,8893963,1610341,369281587,254739,12744926,1444589,832190652,9574702,6247121,20004506,496737560,373372123,21644,760212824,944155252,9581664,901595351,791481283,13987329,603233123,626392058,802140376,11496714,8470680,7724523,4033244,533611788,17164945,825695383,16371556,720747849,396940379,549214725,472227679,533611788,825695383,892449850,994370566,10638101,413720001,15278427,8547148,575363647,478214565,416518755,9501267,369281587,961478933,478214565,802140376,14786208,892449850,8040233,484586129,761424726,752922786,20063863,751510602,7759078,393658973,720747849,733836,982423261,414854327,19054751,484586129,9641926,961478933,960068421,549214725,393658973,725739596,617441992,373372123,761424726,710076313,823455219,472227679,823436946,725739596,455436630,752922786,533611788,802140376,825695383,14733345,496737560,791481283,575363647,752922786,478214565,951262281,396940379,4912435,424483738}

{861729319,15322849,940535029,455436630,25716384,496737560,994370566,424483738,761424726,378070839,575363647,424483738,6756867,15672202,12819727,892449850,751510602,901595351,396940379,2123267,720747849,751510602,944155252,961478933,393658973,966260208,666348,11343259,11356766,533611788,761424726,478214565,28630617,949728057,861729319,18382487,12908508,15973569,960068421,710076313,378070839,25052059,710076313,12276619,760212824,617441992,10217779,413720001,966260208,416518755,396940379,7200078,484586129,966260208,4373644,26498610,608713133,15378286,369281587,5141695,15657782,3888317,455436630,393658973,9578114,455436630,608713133,28043700,961478933,396940379,825695383,752922786,396940379,413720001,951262281,791481283,455436630,412303403,416518755,823436946,413720001,373372123,10264185,966260208,725739596,746001,20166896,951262281,685011884,549214725,617441992,617441992,761424726,16873564,949728057,944155252,15284340,3727561,369281587,6971442,960068421,7072809,8393891,961478933,982423261,994370566,373372123,275259,15511847,825695383,901595351,951262281,940535029,549214725,14837549,861729319,791481283,685011884,787284682,381594,13649520,825695383,472227679,725739596,770373,16415083,861729319,258185,13571757,617441992,20624057,608713133,823436946,4821905,720747849,626392058,357144797,861729319,685011884,951262281,832190652,533611788,12610980,484586129,8393085,802140376,11053657,14978290,823455219,14572206,994370566,760212824,760212824,994370566,575363647,424483738,603233123,549214725,416518755,396940379}

Returns: 36
1000000000

771254575

250687710

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Returns: -1
1000000000

84751923

258320530

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58084,70962597,819271825,659941706,67179537,799623900,817179298,771215068,632357111,776988628,498610185,857294929,432796372,868062849,529362631,885580797,765747960,27921644,674572606,763231922,991050377,806194488,682131142,861301504,48198618,859400291,591046743,546807743,907321836,29352383}

{347247766,445294577,349413523,947638135,14776376,23453482,19924252,622576062,41886388,861495164,772907176,978719300,551749682,678785941,565133272,51590226,981039082,766784140,856799924,477830091,937400155,796433178,885580797,622723740,628333797,71009650,96401000,671438514,780305962,529362631,570484145,873735323,659941706,509241708,632357111,58056234,49608333,799623900,850569794,447856570,681332438,937400155,885580797,23529885,73074202,4578069,466295582,911421331,893556569,5323527,588292475,557039890,987260727,861495164,868062849,975726570,746909652,414362404,40602720,988074723,865361060,618729668,766784140,85911578,905609635,763231922,591046743,17279311,538857779,893680204,445423076,47089727,2964579,985293433,5648207,991746900,64583193,808314528,796777415,936142481,74822765,914625942,675620103,685344751,563223129,794965620,46967901,414362404,414362404,857175144,845580656,565133272,991746900,968377466,674572606,927603231,803149106,28464406,687639089,541495681,68172340,35321223,995130584,445294577,362091287,770319382,58799182,632357111,35661612,721003974,517704969,799468873,884201274,384630692,883761176,65995411,698321178,988074723,797148018,460306689,74659291,413416034,460826871,399274449,25832053,935084960,498610185,968377466,17585079,873865155,927603231,674572606,87785056,886471889,808314528,857294929,919910724,903865336,796069945,409002962,34846378,423615995,350842791,349413523,37284885,780464520,973401019,776988628,489176751,34195009,61149860,577200303,582150820,56656606,82532527,988074723,817179298,432796372,43158364,2824280,91637773,985293433,898391138,400642807,26556506,423865246,659941706,682131142,671861183,516449376,460826871,8412731,29537743,7431755,419805047,489176751,622740886,741051,991746900,395062020,20600308,755938219,15277647,995130584,59270889,861301504,988074723,536537731,927603231,384630692,516449376,26230657,396746401,638336403,622723740,394373068,845580656,973051508,870348124,865361060,893556569,819271825,541495681,492245792,350842791,919910724,738750783,87158268,362091287,33840376,881387687,766784140,52438231,59060283,24992301,24816663,409002962,873865155,884201274,903536974,419256703,44122089,914625942,39701412,13088058,903536974,349413523,591026795,746909652,936142481,46955022,577200303,797148018,42664059,936887987,755622762,780464520,350154812,789082413,65932261,766784140,60771241,536537731,618729668,916999801,934188508,819271825,517704969,819271825,505022526,982080376,591046743,10374929,1946594,796397119,885580797,964756750,712527661,796777415,789082413,2857942,880049703,419805047,66092936,41723945,28196530,753321035,424215581,707961719,742570048,40348319,394373068,30586039,727093074,38113647,16807562,413416034,981039082,536537731,632357111,57503472,39904292,727093074,845580656,47372043,973401019,424215581,975726570,26921735,372368828,435526723,868062849,32212995,820401276,15962062,529362631,47940972,48012243,622740886,505022526,978719300,755938219,395062020,546807743,973051508,987260727,68345706,638336403,44172153,898391138,765747960,86801744,697635308,529362631,364190245,498610185,53739415,24329888,808314528,31698938,721003974,763231922,695345369,570484145,438384234,19487514,455265721,2159987,982080376,477830091,753321035,400894789,981350184,896337930,865361060,913320830,859400291,656451533,349413523,558968887,43324444,685344751,779430615,45957299,13466182,588292475,24905675,485502094,43753504,60484252,372768014,682131142,803149106,905609635,964756750,742679379,6233256,517704969,806194488,14198623,445423076,771215068,865361060,372368828,498234351,613077155,685165094,861301504,671861183,394373068,779430615,796777415,808314528,860749084,632357111,498234351,26921041,438384234,799623900,981350184,873735323,59945035,37154512,727093074,753321035,30483294,577200303,577200303,400642807,988074723,60183951,805674678,883761176,469715831,957439114,957439114,31744844,973401019,399274449,741726881,516449376,21527604,838588160,67069010,8313307,868062849,498610185,350842791,395109129,797148018,72412322,991050377,799623900,849747076,33806922,78520353,973051508,721433898,364190245,395062020,44789055,680612445,765747960,973051508,74990357,886471889,10968875,479056226,47651489,794965620,903865336,621499934,789082413,537374147,742570048,36760877,68537729,819271825,738750783,880049703,55306963,27410578,893556569,589145889,622740886,445294577,455265721,460306689,83353244,10657798,400894789,628333797,12224953,618729668,397564340,803149106,45546454,913320830,919910724,20468908,71178789,803149106,67835523,350842791,936887987,70645897,973401019,64245082,817179298,861495164,509241708,579147196,349413523,69833649,819271825,685165094,845580656,577200303,449379757,485502094,469715831,865361060,615367605,518854867,51314291,498234351,8547639,805674678,19898423,35162777,885580797,410794772,51704825,563223129,43286315,893556569,1953972,797148018,625669688,45595687,727304850,372768014,518854867,43956483,981039082,35446780,16507250,799468873,396746401,856447201,927603231,698321178,68293152,44285055,873735323,577200303,397564340,399274449,498234351,961798376,838588160,995130584,489176751,85034987,466295582,725860391,3119457,621499934,26288451,981350184,477830091,780305962,70256869,32134125,449379757,30628279,881387687,567709375,622576062,784508451,364190245,680612445,3802522,755622762,659941706,50886890,400642807}

Returns: 140
1000000000

20440681

745110000

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Returns: 52
100000000

92315852

93780753

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Returns: -1
1000000000

343423704

767119707

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Returns: -1
1000000000

956416552

277922498

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Returns: 12
1000000000

886608704

71977630

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{80,31,43,33,15,628643571,83,758083839,4,21,2,437569637,641159602,401516789,519088364,585772189,501781279,57,8,88,79,61,762895019,56,86,74,46,9,47,79,515069790,21,31,9,61,44,35,13,80,88,37,33,10,78,60,98,649977296,86,97,846273171,991634055,863232554,85,644683661,39,26,41,519088364,866070336,415161165,497683194,38,446146727,85,51,78,27,41,29,10,29,395017335,49,540757859,9,680885374,42,90,19,50,73,38,938310901,92,54,538716010,8,970819177,450485884,3,56,18,917432617,23,554349628,45,20,74,30,38,3,71,99,57,41,37,66,33,984563859,850200637,8,62,836161663,19,446146727,498833636,46,99,583464637,1,18,24,27,712765546,387023621,16,612789418,550908326,40,51,4,95,7,1,99,17,550908326,21,80,54,11,3,520370908,40,866070336,38,74,44,73,640288269,752607791,859400619,6,48,29,79,340319996,14,97,845436198,77,471793369,367527732,69,984563859,644683661,71,52,59,475148622,978065606,969190758,372151930,60,35,861968872,560597057,55,32,965932642,67,98,32,65,85,57,510073471,57,16,74,396499165,91,70,53,91,78,992366084,26,752607791,470319329,5,769094657,71,500362374,644683661,873655122,479894255,859373864,551627224,67,573844639,436639506,788250970,917432617,512132280,26,71,67,996913758,46,30,745734704,58,11,782114504,755706041,19,849886929,754697055,44,20,49,10,932187253,72,100,791610351,850200637,97,90,25,34,14,80,17,9,503038780,352120304,462236495,47,932187253,15,693786981,510073471,551627224,487133410,37,50,965932642,31,21,83,95,333934634,76,49,96,57,589234987,374609488,43,39,22,56,58,29,620064541,97,919719821,996913758,20,53,96,828887110,436436035,88,81,79,23810,7,34,62,16,29,6,20,4,397142389,63,59,95,80,27,334303236,85,53,55,542095540,503451416,924800822,2,84,753640303,69,5,20,90,67,88,16,901294611,83,647394107,773300700,81,345832336,722607871,57,35,87,34,47,861182403,12,16,636220466,683901864,752610784,500113859,63,45,41,67,99,5,938310901,582115164,837766166,97,82,15,969190758,13,522285626,13,845881031,9,26,8,79,5,29,706405491,683901864,53,857735117,719946154,985960968,10,12,46,15,570352228,4,799713548,32,744839105,23,551262676,74,40,58,575954861,991634055,814262415,73,62,819905080,28,420520602,872956663,643124856,53,56,20,9,68,28,83,5,669109562,989782501,436436035,62,32,83,345228555,78,57,20,47,40,76,503848911,376818690,873655122,47,401516789,97,938310901,58,14,557094501,18,23,26,89,43,66,70,65,546044502,87,33,46,811184980,501129199,21,5,47,487133410,693786981,991770911,41,62,80,41,643124856,38,874736891,640482722,87,82,96,58,18,347055772,75,59,84,43,54,76,23,857585573,95,30,80,45,18,752610784,52,433157832,12,68,49,79,589234987,853422214,548347786,340319996,560597057,937433095,32,22,97,987558875,92,550908326,497683194,3,81,915522055,752607791,651615279,41,799713548,92,54,33,32,75,57,767452426,40,782114504,89,500404448,910267988,100,919719821,719445848,600696322,511469458,75,21,500404448,66,24,569178650,38,55,534192838,29,3,74,51,24,773300700,61,515069790,60,859171275}

Returns: 1
15123123

4726652

10615345

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{5769192,8333,3227,2622,3266,1077,6361,6762,7886922,9725234,5466,3456,6575,17,8606,7398,9996,9055,8495,4558,3720,1262,9645,9130996,3218,7970,3124,6912,2064,6857142,8926,1513,3813,2567,3167,7713,6866956,4294,3450,6404,1658,3529,858,8569,9626,9577,6014,464,1455,4187,8667,4474,1333,2713,506,4365,4193,1504,4435,5030,4485,3533,13451327,9068,7535,13688296,7481,1699,4950,5664,7180,9853,5662389,9745,8705018,539,9006,8679,7542,6199,4685,3712,8043,7204,2913,6067,9558,4517,4306,8877,9520,637,9151397,7529,7607,2362,15066753,2094,2331,6191,4532,9725234,9185,5209,6823,2114,466,7200,9962,7416,4935,6668,10664751,3617,1151,8383,8824038,2746,2027,6512,6665,592,3817,9483,8830,7657,4933,7263,5973,10024,12970071,2457,7805,5693,6410,1804,9228,8719,9654,8824038,2301,9385,6697055,3292,3501,8529,6723,2537,6025,7934,7739,5374,7858,6842,6224,14679452,8755,9667,8822,7546,4588,3009,294,221,6093,9400,3610,4363,1494,7878,104,1795,7676628,10854329,8548,4245,3224,9592,2557,5368,5610,9781,10022,8105,1871,5608,3991,2383,7189,3046,5556,7704,13372081,2275,8795,4378,2444,8748,4648,4168,9815,10051,8538,5488,4729,3756,7865,9935,10048,7828,280,9508696,7587,1453,4900,182,9839,6984,5003,583,58,10083,10019,5104,9151397,528,6401,5287,12,6526,8824038,8217,9897,3737,7430,1330,1648,5892,5433,5250,304,1239,7737,4686,2512,4193,9659,3631,5333,8388,2144,13688296,3958,9454,9430,6722,2567,9425,12148377,1336,4075,14806961,7555,14789815,8995,7343,7633,308,5639,9526930,2314,6823,9036,9190,3729,2140,8211,5854,3516,8848385,11208637,9599,3837,5797,9130996,2400,11523500,9477,4212,2193,5610,15066753,8063,9062,13280818,4269,5056,8406,9744,9894,12636415,3087,7468,5224,2011,9188,8626396,8057,4516,8430,15015959,1121,3816,3629,7275,9480,9582750,5857,6717,7238,2354,5499042,4177,937,11702373,338,5351,6709,10018,1287,5217,6420,4762,1143,1504,5790,8137,3834,3889,813,10820112,5424,6975296,6940,3813,5711,5998,9311,12806036,5092,8780,6059,174,757,6705,6003,6488,7091,3577,5240,5523,2308,4853,8049,685,15104154,5659466,8956,4356,5012,3251,10056,5945998,245,587,6972,3454,7886922,2220,10021,5583,8412,5151,5284,6398,8242,8183,7412,6803,5582,2127,1797,5852,13374152,1820,3717,3055,8848385,3238,9559,1512,8331,690,10554256,8698,6975296,9533,5127,6019,222,8431,5651,6366,6398,6886499,3151,7790,332,8753,123,742,5295,2318,10762769,8436,13372081,30,1132,5263,15108563,7623,9530,8242307,630,1484,3086,6462,8750,10312374,4540,201,53,4284,7158,7498,13280818,5733,6778,6691,4824,572,5072,53885,9786,9508696,1715}

Returns: 3
20000

10007

19699

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19697}

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19699}

Returns: 1000
120000000

10007

19699

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19697}

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19699}

Returns: 793
1337

666

84

{3, 7 }

{35, 15 }

Returns: -1

Statistics

Problem Statement for "FromToDivisible"

Problem Statement

Definition

Constraints

Examples