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: Wrong Answer)

#include <stdio.h>

long modpow(long a, long n, long m){
  long r = 1;
  while(n){
    if(n & 1)  r = (r * a) % m;
    a = (a * a) % m;
    n = n >> 1;
  }
  return r;
}

int main(){
  long mod = 1e9+7;
  long n, p;  scanf("%ld %ld", &n, &p);
  int table[200][2] = {0}, len = 0;
  for(int i=2; i*i<=p; i++){
    if(p%i == 0){
      table[++len][0] = i;
      while(p%i == 0){
	table[len][1]++;
	p /= i;
      }
    }
  }
  if(p != 1){
    table[++len][0] = p;
    table[len][1] = 1;
  }

  long ans = 1;
  for(int i=1; i<=len; i++){
    if(table[i][1]/n){
      ans = (ans * modpow(table[i][0], table[i][1]/n, mod)) % mod;
    }
  }

  printf("%ld\n", ans);
  return 0;
}