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: Runtime Error)

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
typedef long long ll;

ll n, p, i, j, ans;

int main()
{
  scanf("%lld%lld",&n,&p);
  if(n==1)printf("%lld\n",p);
  else if(p==1)printf("1\n");
  else {
    ans=1;
    for(i=0;i<p;i++){
      j=0;while(p%i!=0){p/=i;j++;} if(j/n>0) ans*=pow(i,j/n);
    }
    printf("%lld",ans);
  }
  return 0;
}