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>
int gcd(int a, int b){
    int r;
    r=a%b;
    while(r != 0){
        a=b;
        b=r;
        r=a%b;
    }
    return b;
}
int main(void)
{int g,r,k,j,i,n,p,a[10*10*10*10*10*10];
    j=0;
    scanf("%d %d", &n, &p);
    for(k=1;k<n;k++){
        for(i=2;i<=p;i++){
      if(p % i==0){
        a[j]=i;
        j++;
        p=p/i;
        break;
        }
    }
   }
    a[j]=p;
    if(j>=2)
    g=gcd(gcd(a[j-2], a[j-1]), a[j]);
    if(j==1)
        g=gcd(a[j-1], a[j]);
    if(j==0)
        g=a[j];
    printf("%d\n", g);
    return 0;
}