Problem:


Score : 400 points

Problem Statement

Given are positive integers A and B.

Let us choose some number of positive common divisors of A and B.

Here, any two of the chosen divisors must be coprime.

At most, how many divisors can we choose?

Definition of common divisor

An integer d is said to be a common divisor of integers x and y when d divides both x and y.

Definition of being coprime

Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.

Definition of dividing

An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.

Constraints

All values in input are integers.

1 \leq A, B \leq 10^{12}

Input

Input is given from Standard Input in the following format:

A B

Output

Print the maximum number of divisors that can be chosen to satisfy the condition.

Sample Input 1

12 18

Sample Output 1

3

12 and 18 have the following positive common divisors: 1, 2, 3, and 6.

1 and 2 are coprime, 2 and 3 are coprime, and 3 and 1 are coprime, so we can choose 1, 2, and 3, which achieve the maximum result.

Sample Input 2

420 660

Sample Output 2

4

Sample Input 3

1 2019

Sample Output 3

1

1 and 2019 have no positive common divisors other than 1.



Sample input:
12 18


Sample output:
3

Submission status: Wrong Answer

Solution code:
prime=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 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442457, 442469, 442487, 442489, 442499, 442501, 442517, 442531, 442537, 442571, 442573, 442577, 442579, 442601, 442609, 442619, 442633, 442691, 442699, 442703, 442721, 442733, 442747, 442753, 442763, 442769, 442777, 442781, 442789, 442807, 442817, 442823, 442829, 442831, 442837, 442843, 442861, 442879, 442903, 442919, 442961, 442963, 442973, 442979, 442987, 442991, 442997, 443011, 443017, 443039, 443041, 443057, 443059, 443063, 443077, 443089, 443117, 443123, 443129, 443147, 443153, 443159, 443161, 443167, 443171, 443189, 443203, 443221, 443227, 443231, 443237, 443243, 443249, 443263, 443273, 443281, 443291, 443293, 443341, 443347, 443353, 443363, 443369, 443389, 443407, 443413, 443419, 443423, 443431, 443437, 443453, 443467, 443489, 443501, 443533, 443543, 443551, 443561, 443563, 443567, 443587, 443591, 443603, 443609, 443629, 443659, 443687, 443689, 443701, 443711, 443731, 443749, 443753, 443759, 443761, 443771, 443777, 443791, 443837, 443851, 443867, 443869, 443873, 443879, 443881, 443893, 443899, 443909, 443917, 443939, 443941, 443953, 443983, 443987, 443999, 444001, 444007, 444029, 444043, 444047, 444079, 444089, 444109, 444113, 444121, 444127, 444131, 444151, 444167, 444173, 444179, 444181, 444187, 444209, 444253, 444271, 444281, 444287, 444289, 444293, 444307, 444341, 444343, 444347, 444349, 444401, 444403, 444421, 444443, 444449, 444461, 444463, 444469, 444473, 444487, 444517, 444523, 444527, 444529, 444539, 444547, 444553, 444557, 444569, 444589, 444607, 444623, 444637, 444641, 444649, 444671, 444677, 444701, 444713, 444739, 444767, 444791, 444793, 444803, 444811, 444817, 444833, 444841, 444859, 444863, 444869, 444877, 444883, 444887, 444893, 444901, 444929, 444937, 444953, 444967, 444971, 444979, 445001, 445019, 445021, 445031, 445033, 445069, 445087, 445091, 445097, 445103, 445141, 445157, 445169, 445183, 445187, 445199, 445229, 445261, 445271, 445279, 445283, 445297, 445307, 445321, 445339, 445363, 445427, 445433, 445447, 445453, 445463, 445477, 445499, 445507, 445537, 445541, 445567, 445573, 445583, 445589, 445597, 445619, 445631, 445633, 445649, 445657, 445691, 445699, 445703, 445741, 445747, 445769, 445771, 445789, 445799, 445807, 445829, 445847, 445853, 445871, 445877, 445883, 445891, 445931, 445937, 445943, 445967, 445969, 446003, 446009, 446041, 446053, 446081, 446087, 446111, 446123, 446129, 446141, 446179, 446189, 446191, 446197, 446221, 446227, 446231, 446261, 446263, 446273, 446279, 446293, 446309, 446323, 446333, 446353, 446363, 446387, 446389, 446399, 446401, 446417, 446441, 446447, 446461, 446473, 446477, 446503, 446533, 446549, 446561, 446569, 446597, 446603, 446609, 446647, 446657, 446713, 446717, 446731, 446753, 446759, 446767, 446773, 446819, 446827, 446839, 446863, 446881, 446891, 446893, 446909, 446911, 446921, 446933, 446951, 446969, 446983, 447001, 447011, 447019, 447053, 447067, 447079, 447101, 447107, 447119, 447133, 447137, 447173, 447179, 447193, 447197, 447211, 447217, 447221, 447233, 447247, 447257, 447259, 447263, 447311, 447319, 447323, 447331, 447353, 447401, 447409, 447427, 447439, 447443, 447449, 447451, 447463, 447467, 447481, 447509, 447521, 447527, 447541, 447569, 447571, 447611, 447617, 447637, 447641, 447677, 447683, 447701, 447703, 447743, 447749, 447757, 447779, 447791, 447793, 447817, 447823, 447827, 447829, 447841, 447859, 447877, 447883, 447893, 447901, 447907, 447943, 447961, 447983, 447991, 448003, 448013, 448027, 448031, 448057, 448067, 448073, 448093, 448111, 448121, 448139, 448141, 448157, 448159, 448169, 448177, 448187, 448193, 448199, 448207, 448241, 448249, 448303, 448309, 448313, 448321, 448351, 448363, 448367, 448373, 448379, 448387, 448397, 448421, 448451, 448519, 448531, 448561, 448597, 448607, 448627, 448631, 448633, 448667, 448687, 448697, 448703, 448727, 448733, 448741, 448769, 448793, 448801, 448807, 448829, 448843, 448853, 448859, 448867, 448871, 448873, 448879, 448883, 448907, 448927, 448939, 448969, 448993, 448997, 448999, 449003, 449011, 449051, 449077, 449083, 449093, 449107, 449117, 449129, 449131, 449149, 449153, 449161, 449171, 449173, 449201, 449203, 449209, 449227, 449243, 449249, 449261, 449263, 449269, 449287, 449299, 449303, 449311, 449321, 449333, 449347, 449353, 449363, 449381, 449399, 449411, 449417, 449419, 449437, 449441, 449459, 449473, 449543, 449549, 449557, 449563, 449567, 449569, 449591, 449609, 449621, 449629, 449653, 449663, 449671, 449677, 449681, 449689, 449693, 449699, 449741, 449759, 449767, 449773, 449783, 449797, 449807, 449821, 449833, 449851, 449879, 449921, 449929, 449941, 449951, 449959, 449963, 449971, 449987, 449989, 450001, 450011, 450019, 450029, 450067, 450071, 450077, 450083, 450101, 450103, 450113, 450127, 450137, 450161, 450169, 450193, 450199, 450209, 450217, 450223, 450227, 450239, 450257, 450259, 450277, 450287, 450293, 450299, 450301, 450311, 450343, 450349, 450361, 450367, 450377, 450383, 450391, 450403, 450413, 450421, 450431, 450451, 450473, 450479, 450481, 450487, 450493, 450503, 450529, 450533, 450557, 450563, 450581, 450587, 450599, 450601, 450617, 450641, 450643, 450649, 450677, 450691, 450707, 450719, 450727, 450761, 450767, 450787, 450797, 450799, 450803, 450809, 450811, 450817, 450829, 450839, 450841, 450847, 450859, 450881, 450883, 450887, 450893, 450899, 450913, 450917, 450929, 450943, 450949, 450971, 450991, 450997, 451013, 451039, 451051, 451057, 451069, 451093, 451097, 451103, 451109, 451159, 451177, 451181, 451183, 451201, 451207, 451249, 451277, 451279, 451301, 451303, 451309, 451313, 451331, 451337, 451343, 451361, 451387, 451397, 451411, 451439, 451441, 451481, 451499, 451519, 451523, 451541, 451547, 451553, 451579, 451601, 451609, 451621, 451637, 451657, 451663, 451667, 451669, 451679, 451681, 451691, 451699, 451709, 451723, 451747, 451753, 451771, 451783, 451793, 451799, 451823, 451831, 451837, 451859, 451873, 451879, 451897, 451901, 451903, 451909, 451921, 451933, 451937, 451939, 451961, 451967, 451987, 452009, 452017, 452027, 452033, 452041, 452077, 452083, 452087, 452131, 452159, 452161, 452171, 452191, 452201, 452213, 452227, 452233, 452239, 452269, 452279, 452293, 452297, 452329, 452363, 452377, 452393, 452401, 452443, 452453, 452497, 452519, 452521, 452531, 452533, 452537, 452539, 452549, 452579, 452587, 452597, 452611, 452629, 452633, 452671, 452687, 452689, 452701, 452731, 452759, 452773, 452797, 452807, 452813, 452821, 452831, 452857, 452869, 452873, 452923, 452953, 452957, 452983, 452989, 453023, 453029, 453053, 453073, 453107, 453119, 453133, 453137, 453143, 453157, 453161, 453181, 453197, 453199, 453209, 453217, 453227, 453239, 453247, 453269, 453289, 453293, 453301, 453311, 453317, 453329, 453347, 453367, 453371, 453377, 453379, 453421, 453451, 453461, 453527, 453553, 453559, 453569, 453571, 453599, 453601, 453617, 453631, 453637, 453641, 453643, 453659, 453667, 453671, 453683, 453703, 453707, 453709, 453737, 453757, 453797, 453799, 453823, 453833, 453847, 453851, 453877, 453889, 453907, 453913, 453923, 453931, 453949, 453961, 453977, 453983, 453991, 454009, 454021, 454031, 454033, 454039, 454061, 454063, 454079, 454109, 454141, 454151, 454159, 454183, 454199, 454211, 454213, 454219, 454229, 454231, 454247, 454253, 454277, 454297, 454303, 454313, 454331, 454351, 454357, 454361, 454379, 454387, 454409, 454417, 454451, 454453, 454483, 454501, 454507, 454513, 454541, 454543, 454547, 454577, 454579, 454603, 454609, 454627, 454637, 454673, 454679, 454709, 454711, 454721, 454723, 454759, 454763, 454777, 454799, 454823, 454843, 454847, 454849, 454859, 454889, 454891, 454907, 454919, 454921, 454931, 454943, 454967, 454969, 454973, 454991, 455003, 455011, 455033, 455047, 455053, 455093, 455099, 455123, 455149, 455159, 455167, 455171, 455177, 455201, 455219, 455227, 455233, 455237, 455261, 455263, 455269, 455291, 455309, 455317, 455321, 455333, 455339, 455341, 455353, 455381, 455393, 455401, 455407, 455419, 455431, 455437, 455443, 455461, 455471, 455473, 455479, 455489, 455491, 455513, 455527, 455531, 455537, 455557, 455573, 455579, 455597, 455599, 455603, 455627, 455647, 455659, 455681, 455683, 455687, 455701, 455711, 455717, 455737, 455761, 455783, 455789, 455809, 455827, 455831, 455849, 455863, 455881, 455899, 455921, 455933, 455941, 455953, 455969, 455977, 455989, 455993, 455999, 456007, 456013, 456023, 456037, 456047, 456061, 456091, 456107, 456109, 456119, 456149, 456151, 456167, 456193, 456223, 456233, 456241, 456283, 456293, 456329, 456349, 456353, 456367, 456377, 456403, 456409, 456427, 456439, 456451, 456457, 456461, 456499, 456503, 456517, 456523, 456529, 456539, 456553, 456557, 456559, 456571, 456581, 456587, 456607, 456611, 456613, 456623, 456641, 456647, 456649, 456653, 456679, 456683, 456697, 456727, 456737, 456763, 456767, 456769, 456791, 456809, 456811, 456821, 456871, 456877, 456881, 456899, 456901, 456923, 456949, 456959, 456979, 456991, 457001, 457003, 457013, 457021, 457043, 457049, 457057, 457087, 457091, 457097, 457099, 457117, 457139, 457151, 457153, 457183, 457189, 457201, 457213, 457229, 457241, 457253, 457267, 457271, 457277, 457279, 457307, 457319, 457333, 457339, 457363, 457367, 457381, 457393, 457397, 457399, 457403, 457411, 457421, 457433, 457459, 457469, 457507, 457511, 457517, 457547, 457553, 457559, 457571, 457607, 457609, 457621, 457643, 457651, 457661, 457669, 457673, 457679, 457687, 457697, 457711, 457739, 457757, 457789, 457799, 457813, 457817, 457829, 457837, 457871, 457889, 457903, 457913, 457943, 457979, 457981, 457987, 458009, 458027, 458039, 458047, 458053, 458057, 458063, 458069, 458119, 458123, 458173, 458179, 458189, 458191, 458197, 458207, 458219, 458239, 458309, 458317, 458323, 458327, 458333, 458357, 458363, 458377, 458399, 458401, 458407, 458449, 458477, 458483, 458501, 458531, 458533, 458543, 458567, 458569, 458573, 458593, 458599, 458611, 458621, 458629, 458639, 458651, 458663, 458669, 458683, 458701, 458719, 458729, 458747, 458789, 458791, 458797, 458807, 458819, 458849, 458863, 458879, 458891, 458897, 458917, 458921, 458929, 458947, 458957, 458959, 458963, 458971, 458977, 458981, 458987, 458993, 459007, 459013, 459023, 459029, 459031, 459037, 459047, 459089, 459091, 459113, 459127, 459167, 459169, 459181, 459209, 459223, 459229, 459233, 459257, 459271, 459293, 459301, 459313, 459317, 459337, 459341, 459343, 459353, 459373, 459377, 459383, 459397, 459421, 459427, 459443, 459463, 459467, 459469, 459479, 459509, 459521, 459523, 459593, 459607, 459611, 459619, 459623, 459631, 459647, 459649, 459671, 459677, 459691, 459703, 459749, 459763, 459791, 459803, 459817, 459829, 459841, 459847, 459883, 459913, 459923, 459929, 459937, 459961, 460013, 460039, 460051, 460063, 460073, 460079, 460081, 460087, 460091, 460099, 460111, 460127, 460147, 460157, 460171, 460181, 460189, 460211, 460217, 460231, 460247, 460267, 460289, 460297, 460301, 460337, 460349, 460373, 460379, 460387, 460393, 460403, 460409, 460417, 460451, 460463, 460477, 460531, 460543, 460561, 460571, 460589, 460609, 460619, 460627, 460633, 460637, 460643, 460657, 460673, 460697, 460709, 460711, 460721, 460771, 460777, 460787, 460793, 460813, 460829, 460841, 460843, 460871, 460891, 460903, 460907, 460913, 460919, 460937, 460949, 460951, 460969, 460973, 460979, 460981, 460987, 460991, 461009, 461011, 461017, 461051, 461053, 461059, 461093, 461101, 461119, 461143, 461147, 461171, 461183, 461191, 461207, 461233, 461239, 461257, 461269, 461273, 461297, 461299, 461309, 461317, 461323, 461327, 461333, 461359, 461381, 461393, 461407, 461411, 461413, 461437, 461441, 461443, 461467, 461479, 461507, 461521, 461561, 461569, 461581, 461599, 461603, 461609, 461627, 461639, 461653, 461677, 461687, 461689, 461693, 461707, 461717, 461801, 461803, 461819, 461843, 461861, 461887, 461891, 461917, 461921, 461933, 461957, 461971, 461977, 461983, 462013, 462041, 462067, 462073, 462079, 462097, 462103, 462109, 462113, 462131, 462149, 462181, 462191, 462199, 462221, 462239, 462263, 462271, 462307, 462311, 462331, 462337, 462361, 462373, 462377, 462401, 462409, 462419, 462421, 462437, 462443, 462467, 462481, 462491, 462493, 462499, 462529, 462541, 462547, 462557, 462569, 462571, 462577, 462589, 462607, 462629, 462641, 462643, 462653, 462659, 462667, 462673, 462677, 462697, 462713, 462719, 462727, 462733, 462739, 462773, 462827, 462841, 462851, 462863, 462871, 462881, 462887, 462899, 462901, 462911, 462937, 462947, 462953, 462983, 463003, 463031, 463033, 463093, 463103, 463157, 463181, 463189, 463207, 463213, 463219, 463231, 463237, 463247, 463249, 463261, 463283, 463291, 463297, 463303, 463313, 463319, 463321, 463339, 463343, 463363, 463387, 463399, 463433, 463447, 463451, 463453, 463457, 463459, 463483, 463501, 463511, 463513, 463523, 463531, 463537, 463549, 463579, 463613, 463627, 463633, 463643, 463649, 463663, 463679, 463693, 463711, 463717, 463741, 463747, 463753, 463763, 463781, 463787, 463807, 463823, 463829, 463831, 463849, 463861, 463867, 463873, 463889, 463891, 463907, 463919, 463921, 463949]
a,b=[int(i) for i in input().split()]
ans=1
for i in prime:
    if a%i==0 and b%i==0:
        ans+=1
print(ans)