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 9.2.1) (judge verdict: Accepted)

#include <stdio.h>
int main(){
  long long n,p,f[99],a[99],ans=1,c,i,x=0;
  scanf("%lld%lld",&n,&p);
  for(i=2;i*i<=p;i++){c=0;while(p%i==0){p/=i;c++;}if(c){f[x]=i;a[x++]=c;}}
  if(p-1){f[x]=p;a[x++]=1;}
  for(i=0;i<x;i++)for(c=1;c*n<=a[i];c++)ans*=f[i]; 
  printf("%lld",ans);
}