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: Accepted)

#include<stdio.h>

typedef long long int int64;

void run(void){
  int64 n,p;
  scanf("%lld%lld",&n,&p);
  if(n==1){
    printf("%lld\n",p);
    return;
  }
  int64 ans=1;
  int64 k;
  for(k=2;k*k<=p;k++){
    int c=0;
    while(p%k==0){
      p/=k;
      c++;
    }
    c/=n;
    while(c--){
      ans*=k;
    }
  }
  printf("%lld\n",ans);
}

int main(void){
  run();
  return 0;
}