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 <stdio.h>
#include <stdlib.h>

int main(void)
{
      int n,p,a,b,c,i = 0,j = 0,ans = 1;
      scanf("%d %d",&n,&p);
      int q = p;
      int A[p + 1];

      for(i = 0;i < p + 1;i++) A[i] = 0;

      i = 0;
      for(i = 2;i< p + 1;i++) {
            j = 0;

            while(j < 10000) {
                  if(q % i  == 0) {
                        q = q / i;
//                        printf("q %d\n",q);
                        j++;
                  } else {
                        break;
                  }

            }

            A[i] = j;
      }

      i = 0;
      for(i = 0;i<p + 1;i++) {
//          printf("A[%d] %d\n",i,A[i]);

            while(1) {

                  if(A[i] >= n) {
                        ans = ans * i;
                        A[i] = A[i] - n;
                  } else if (A[i] < n) {
                        break;
                  }

           }

      }

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

      return 0;
}