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

Solution in C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;

long long N, P;
vector<long long> prime_factor; // 含まれる素因数
map<long long, long long> factor; // <Mの素因数, その個数>
long long sosuu[] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,8263,8269,8273,8287,8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51,491261,491273,491279,491297,491299,491327,491329,491333,491339,491341,491353,491357,491371,491377,491417,491423,491429,491461,491483,491489,491497,491501,491503,491527,491531,491537,491539,491581,491591,491593,491611,491627,491633,491639,491651,491653,491669,491677,491707,491719,491731,491737,491747,491773,491783,491789,491797,491819,491833,491837,491851,491857,491867,491873,491899,491923,491951,491969,491977,491983,492007,492013,492017,492029,492047,492053,492059,492061,492067,492077,492083,492103,492113,492227,492251,492253,492257,492281,492293,492299,492319,492377,492389,492397,492403,492409,492413,492421,492431,492463,492467,492487,492491,492511,492523,492551,492563,492587,492601,492617,492619,492629,492631,492641,492647,492659,492671,492673,492707,492719,492721,492731,492757,492761,492763,492769,492781,492799,492839,492853,492871,492883,492893,492901,492911,492967,492979,493001,493013,493021,493027,493043,493049,493067,493093,493109,493111,493121,493123,493127,493133,493139,493147,493159,493169,493177,493193,493201,493211,493217,493219,493231,493243,493249,493277,493279,493291,493301,493313,493333,493351,493369,493393,493397,493399,493403,493433,493447,493457,493463,493481,493523,493531,493541,493567,493573,493579,493583,493607,493621,493627,493643,493657,493693,493709,493711,493721,493729,493733,493747,493777,493793,493807,493811,493813,493817,493853,493859,493873,493877,493897,493919,493931,493937,493939,493967,493973,493979,493993,494023,494029,494041,494051,494069,494077,494083,494093,494101,494107,494129,494141,494147,494167,494191,494213,494237,494251,494257,494267,494269,494281,494287,494317,494327,494341,494353,494359,494369,494381,494383,494387,494407,494413,494441,494443,494471,494497,494519,494521,494539,494561,494563,494567,494587,494591,494609,494617,494621,494639,494647,494651,494671,494677,494687,494693,494699,494713,494719,494723,494731,494737,494743,494749,494759,494761,494783,494789,494803,494843,494849,494873,494899,494903,494917,494927,494933,494939,494959,494987,495017,495037,495041,495043,495067,495071,495109,495113,495119,495133,495139,495149,495151,495161,495181,495199,495211,495221,495241,495269,495277,495289,495301,495307,495323,495337,495343,495347,495359,495361,495371,495377,495389,495401,495413,495421,495433,495437,495449,495457,495461,495491,495511,495527,495557,495559,495563,495569,495571,495587,495589,495611,495613,495617,495619,495629,495637,495647,495667,495679,495701,495707,495713,495749,495751,495757,495769,495773,495787,495791,495797,495799,495821,495827,495829,495851,495877,495893,495899,495923,495931,495947,495953,495959,495967,495973,495983,496007,496019,496039,496051,496063,496073,496079,496123,496127,496163,496187,496193,496211,496229,496231,496259,496283,496289,496291,496297,496303,496313,496333,496339,496343,496381,496399,496427,496439,496453,496459,496471,496477,496481,496487,496493,496499,496511,496549,496579,496583,496609,496631,496669,496681,496687,496703,496711,496733,496747,496763,496789,496813,496817,496841,496849,496871,496877,496889,496891,496897,496901,496913,496919,496949,496963,496997,496999,497011,497017,497041,497047,497051,497069,497093,497111,497113,497117,497137,497141,497153,497171,497177,497197,497239,497257,497261,497269,497279,497281,497291,497297,497303,497309,497323,497339,497351,497389,497411,497417,497423,497449,497461,497473,497479,497491,497501,497507,497509,497521,497537,497551,497557,497561,497579,497587,497597,497603,497633,497659,497663,497671,497677,497689,497701,497711,497719,497729,497737,497741,497771,497773,497801,497813,497831,497839,497851,497867,497869,497873,497899,497929,497957,497963,497969,497977,497989,497993,497999,498013,498053,498061,498073,498089,498101,498103,498119,498143,498163,498167,498181,498209,498227,498257,498259,498271,498301,498331,498343,498361,498367,498391,498397,498401,498403,498409,498439,498461,498467,498469,498493,498497,498521,498523,498527,498551,498557,498577,498583,498599,498611,498613,498643,498647,498653,498679,498689,498691,498733,498739,498749,498761,498767,498779,498781,498787,498791,498803,498833,498857,498859,498881,498907,498923,498931,498937,498947,498961,498973,498977,498989,499021,499027,499033,499039,499063,499067,499099,499117,499127,499129,499133,499139,499141,499151,499157,499159,499181,499183,499189,499211,499229,499253,499267,499277,499283,499309,499321,499327,499349,499361,499363,499391,499397,499403,499423,499439,499459,499481,499483,499493,499507,499519,499523,499549,499559,499571,499591,499601,499607,499621,499633,499637,499649,499661,499663,499669,499673,499679,499687,499691,499693,499711,499717,499729,499739,499747,499781,499787,499801,499819,499853,499879,499883,499897,499903,499927,499943,499957,499969,499973,499979};

void Factorize(long long M) {
  int a = 0;
  while (M >= sosuu[a] * sosuu[a]) {
    if (M % sosuu[a] == 0) {
      if (factor[sosuu[a]] == 0) {
        prime_factor.push_back(sosuu[a]);
      }
      factor[sosuu[a]]++;
      M /= sosuu[a];
    } else {
      if (sosuu[a] == 499979) {
        break;
      } else {
        a++;
      }
    }
  }
  int b = 500000;
  while (M >= b * b) {
    if (M % b == 0) {
      if (factor[b] == 0) {
        prime_factor.push_back(b);
      }
      factor[b]++;
      M /= b;
    } else {
      b++;
    }
  }
  if (factor[M] == 0) {
    prime_factor.push_back(M);
  }
  factor[M]++;
}

int main() {
  cin >> N >> P;
  if (N == 1) {
    cout << P << endl;
    return 0;
  }
  Factorize(P);
  long long ans = 1;
  for (int i = 0; i < prime_factor.size(); i++) {
    while (factor[prime_factor[i]] >= N) {
      ans *= prime_factor[i];
      factor[prime_factor[i]] -= N;
    }
  }
  cout << ans << endl;
}