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: Wrong Answer)

#include<stdio.h>
#include<math.h>

int main(){
  double N, P, c;

  scanf("%lf %lf", &N, &P);
  if(N == 1){
    printf("%.0lf\n", P);
    return 0;
  }

  long long i, ans;

  double r = 1;

  ans = 1;

  for(i = 1; i <= pow(P, 1/N); i++){
    if((long long int)P % (long long int)i == 0) c = pow(i, N);
    if(c > P) break;
    if((long long int)P % (long long int)c == 0) ans = i;
  }

  printf("%lld\n", ans);
  
  return 0;
}