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 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>

int main(){
  long long int n, p;
  long long int i, j, g, ans;

  scanf("%lld %lld", &n, &p);

  ans = 1;
  for (i = 2; i <= p / n*n; i++) {
    g = 1;
    for (j = 1; j <= n; j++) {
      g = g * i;
      if (g > p) {
        break;
      }
    }
    if (p % g == 0) {
      ans = i;
    }
    if (g > p) {
      break;
    }
  }

  printf("%lld\n", ans);

  return 0;
}