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: Accepted)

#include <bits/stdc++.h>
using namespace std;

#define DEBUG(x) cout << "DEBUG>" << #x << ":" << x << endl;
#define REP(i,n) for(long long i=0;i<(n);i++)
#define FOR(i,a,b) for(long long i=(a);i<=(b);i++)

int main() {
  long long N, P;
  cin >> N >> P;
  map<long long, long long> res;
  long long ans = 1;
  for(long long i = 2; i * i <= P; i++) {
    while(P % i == 0) {
      res[i]++;
      P /= i;
    }
    if(res[i] >= N) {
      long long a = (res[i] - res[i] % N) / N;
      REP(j, a) {
        ans *= i;
      }
    }
  }
  if(P != 1) {
    res[P] = 1;
    if(res[P] >= N) {
      ans *= P;
    }
  }
  cout << ans << endl;
  return 0;
}