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 <math.h>
#define LIMIT 1000010

int main(void){
  long long N, P;
  scanf("%lld%lld", &N, &P);
  
  long long insu[LIMIT];
  for (long long i = 0; i < LIMIT; i++) {
    insu[i] = 0;
  }

  for (long long i = 2; i < LIMIT && P > 1; i++) {
    while(P%i == 0){
      insu[i]++;
      P /= i;
    }
  }

  long long ans = 1;
  for (long long i = 0; i < LIMIT; i++) {
    while(insu[i] >= N){
      ans *= i;
      insu[i] -= N;
    }
  }

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

  return 0;
}