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: Runtime Error)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>

typedef long long ll;

int t[100000];
int k[300007];

int main(){
  ll n,m;
  ll p;
  int sp = 0;
  int a,i;
  ll ans = 1;
  int limit;

  scanf("%lld %lld", &n, &p);

  for(i = 0;i <= 300000;i++) k[i] = 0;

  if(n == 1){
    printf("%lld\n", p);
    return 0;
  }

  if(p == 1 || p == 2 || p == 3){
    printf("%lld\n", p);
    return 0;
  }

  limit = sqrt(p);

  for(i = 2;i <= limit;i++){
    while(p % i == 0){
      k[i]++;
      p = p/i;
    }
  }

  for(i = 2;i <= 300000;i++){
    ans = ans*pow(i,(k[i])/n);
  }

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

  return 0;
}