Problem:


Score : 300 points

Problem Statement

There are N integers a_1, a_2, ..., a_N not less than 1.
The values of a_1, a_2, ..., a_N are not known, but it is known that a_1 \times a_2 \times ... \times a_N = P.

Find the maximum possible greatest common divisor of a_1, a_2, ..., a_N.

Constraints

1 \leq N \leq 10^{12}

1 \leq P \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N P

Output

Print the answer.

Sample Input 1

3 24

Sample Output 1

2

The greatest common divisor would be 2 when, for example, a_1=2, a_2=6 and a_3=2.

Sample Input 2

5 1

Sample Output 2

1

As a_i are positive integers, the only possible case is a_1 = a_2 = a_3 = a_4 = a_5 = 1.

Sample Input 3

1 111

Sample Output 3

111

Sample Input 4

4 972439611840

Sample Output 4

206



Sample input:
3 24


Sample output:
2

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, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 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987979, 987983, 987991, 987997, 988007, 988021, 988033, 988051, 988061, 988067, 988069, 988093, 988109, 988111, 988129, 988147, 988157, 988199, 988213, 988217, 988219, 988231, 988237, 988243, 988271, 988279, 988297, 988313, 988319, 988321, 988343, 988357, 988367, 988409, 988417, 988439, 988453, 988459, 988483, 988489, 988501, 988511, 988541, 988549, 988571, 988577, 988579, 988583, 988591, 988607, 988643, 988649, 988651, 988661, 988681, 988693, 988711, 988727, 988733, 988759, 988763, 988783, 988789, 988829, 988837, 988849, 988859, 988861, 988877, 988901, 988909, 988937, 988951, 988963, 988979, 989011, 989029, 989059, 989071, 989081, 989099, 989119, 989123, 989171, 989173, 989231, 989239, 989249, 989251, 989279, 989293, 989309, 989321, 989323, 989327, 989341, 989347, 989353, 989377, 989381, 989411, 989419, 989423, 989441, 989467, 989477, 989479, 989507, 989533, 989557, 989561, 989579, 989581, 989623, 989629, 989641, 989647, 989663, 989671, 989687, 989719, 989743, 989749, 989753, 989761, 989777, 989783, 989797, 989803, 989827, 989831, 989837, 989839, 989869, 989873, 989887, 989909, 989917, 989921, 989929, 989939, 989951, 989959, 989971, 989977, 989981, 989999, 990001, 990013, 990023, 990037, 990043, 990053, 990137, 990151, 990163, 990169, 990179, 990181, 990211, 990239, 990259, 990277, 990281, 990287, 990289, 990293, 990307, 990313, 990323, 990329, 990331, 990349, 990359, 990361, 990371, 990377, 990383, 990389, 990397, 990463, 990469, 990487, 990497, 990503, 990511, 990523, 990529, 990547, 990559, 990589, 990593, 990599, 990631, 990637, 990643, 990673, 990707, 990719, 990733, 990761, 990767, 990797, 990799, 990809, 990841, 990851, 990881, 990887, 990889, 990893, 990917, 990923, 990953, 990961, 990967, 990973, 990989, 991009, 991027, 991031, 991037, 991043, 991057, 991063, 991069, 991073, 991079, 991091, 991127, 991129, 991147, 991171, 991181, 991187, 991201, 991217, 991223, 991229, 991261, 991273, 991313, 991327, 991343, 991357, 991381, 991387, 991409, 991427, 991429, 991447, 991453, 991483, 991493, 991499, 991511, 991531, 991541, 991547, 991567, 991579, 991603, 991607, 991619, 991621, 991633, 991643, 991651, 991663, 991693, 991703, 991717, 991723, 991733, 991741, 991751, 991777, 991811, 991817, 991867, 991871, 991873, 991883, 991889, 991901, 991909, 991927, 991931, 991943, 991951, 991957, 991961, 991973, 991979, 991981, 991987, 991999, 992011, 992021, 992023, 992051, 992087, 992111, 992113, 992129, 992141, 992153, 992179, 992183, 992219, 992231, 992249, 992263, 992267, 992269, 992281, 992309, 992317, 992357, 992359, 992363, 992371, 992393, 992417, 992429, 992437, 992441, 992449, 992461, 992513, 992521, 992539, 992549, 992561, 992591, 992603, 992609, 992623, 992633, 992659, 992689, 992701, 992707, 992723, 992737, 992777, 992801, 992809, 992819, 992843, 992857, 992861, 992863, 992867, 992891, 992903, 992917, 992923, 992941, 992947, 992963, 992983, 993001, 993011, 993037, 993049, 993053, 993079, 993103, 993107, 993121, 993137, 993169, 993197, 993199, 993203, 993211, 993217, 993233, 993241, 993247, 993253, 993269, 993283, 993287, 993319, 993323, 993341, 993367, 993397, 993401, 993407, 993431, 993437, 993451, 993467, 993479, 993481, 993493, 993527, 993541, 993557, 993589, 993611, 993617, 993647, 993679, 993683, 993689, 993703, 993763, 993779, 993781, 993793, 993821, 993823, 993827, 993841, 993851, 993869, 993887, 993893, 993907, 993913, 993919, 993943, 993961, 993977, 993983, 993997, 994013, 994027, 994039, 994051, 994067, 994069, 994073, 994087, 994093, 994141, 994163, 994181, 994183, 994193, 994199, 994229, 994237, 994241, 994247, 994249, 994271, 994297, 994303, 994307, 994309, 994319, 994321, 994337, 994339, 994363, 994369, 994391, 994393, 994417, 994447, 994453, 994457, 994471, 994489, 994501, 994549, 994559, 994561, 994571, 994579, 994583, 994603, 994621, 994657, 994663, 994667, 994691, 994699, 994709, 994711, 994717, 994723, 994751, 994769, 994793, 994811, 994813, 994817, 994831, 994837, 994853, 994867, 994871, 994879, 994901, 994907, 994913, 994927, 994933, 994949, 994963, 994991, 994997, 995009, 995023, 995051, 995053, 995081, 995117, 995119, 995147, 995167, 995173, 995219, 995227, 995237, 995243, 995273, 995303, 995327, 995329, 995339, 995341, 995347, 995363, 995369, 995377, 995381, 995387, 995399, 995431, 995443, 995447, 995461, 995471, 995513, 995531, 995539, 995549, 995551, 995567, 995573, 995587, 995591, 995593, 995611, 995623, 995641, 995651, 995663, 995669, 995677, 995699, 995713, 995719, 995737, 995747, 995783, 995791, 995801, 995833, 995881, 995887, 995903, 995909, 995927, 995941, 995957, 995959, 995983, 995987, 995989, 996001, 996011, 996019, 996049, 996067, 996103, 996109, 996119, 996143, 996157, 996161, 996167, 996169, 996173, 996187, 996197, 996209, 996211, 996253, 996257, 996263, 996271, 996293, 996301, 996311, 996323, 996329, 996361, 996367, 996403, 996407, 996409, 996431, 996461, 996487, 996511, 996529, 996539, 996551, 996563, 996571, 996599, 996601, 996617, 996629, 996631, 996637, 996647, 996649, 996689, 996703, 996739, 996763, 996781, 996803, 996811, 996841, 996847, 996857, 996859, 996871, 996881, 996883, 996887, 996899, 996953, 996967, 996973, 996979, 997001, 997013, 997019, 997021, 997037, 997043, 997057, 997069, 997081, 997091, 997097, 997099, 997103, 997109, 997111, 997121, 997123, 997141, 997147, 997151, 997153, 997163, 997201, 997207, 997219, 997247, 997259, 997267, 997273, 997279, 997307, 997309, 997319, 997327, 997333, 997343, 997357, 997369, 997379, 997391, 997427, 997433, 997439, 997453, 997463, 997511, 997541, 997547, 997553, 997573, 997583, 997589, 997597, 997609, 997627, 997637, 997649, 997651, 997663, 997681, 997693, 997699, 997727, 997739, 997741, 997751, 997769, 997783, 997793, 997807, 997811, 997813, 997877, 997879, 997889, 997891, 997897, 997933, 997949, 997961, 997963, 997973, 997991, 998009, 998017, 998027, 998029, 998069, 998071, 998077, 998083, 998111, 998117, 998147, 998161, 998167, 998197, 998201, 998213, 998219, 998237, 998243, 998273, 998281, 998287, 998311, 998329, 998353, 998377, 998381, 998399, 998411, 998419, 998423, 998429, 998443, 998471, 998497, 998513, 998527, 998537, 998539, 998551, 998561, 998617, 998623, 998629, 998633, 998651, 998653, 998681, 998687, 998689, 998717, 998737, 998743, 998749, 998759, 998779, 998813, 998819, 998831, 998839, 998843, 998857, 998861, 998897, 998909, 998917, 998927, 998941, 998947, 998951, 998957, 998969, 998983, 998989, 999007, 999023, 999029, 999043, 999049, 999067, 999083, 999091, 999101, 999133, 999149, 999169, 999181, 999199, 999217, 999221, 999233, 999239, 999269, 999287, 999307, 999329, 999331, 999359, 999371, 999377, 999389, 999431, 999433, 999437, 999451, 999491, 999499, 999521, 999529, 999541, 999553, 999563, 999599, 999611, 999613, 999623, 999631, 999653, 999667, 999671, 999683, 999721, 999727, 999749, 999763, 999769, 999773, 999809, 999853, 999863, 999883, 999907, 999917, 999931, 999953, 999959, 999961, 999979, 999983]

n,p = map(int, input().split())

ans = 1

for x in prime:
    if p%x == 0:
        tp = p
        tmp = 0
        while tp%x == 0:
            tmp += 1
            tp = tp // x
        ans = ans * x**int(tmp/n)

print(ans)