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>
#include <sysexits.h>
#include<stdlib.h>
#include<math.h>
int main(void){
  int sum,i,h;
  double g,N,P;
  sum=1;
  if(scanf("%lf%lf",&N,&P)>2){
    exit(0);
    }
   for(i=1;i<P;i++){
      g=P/pow(i,N);
      h=g;
      if(h==g && g >= 1){
        sum=i;
      }
      if(g<1) break;
    }
    printf("%d",sum);
  return 0;
}