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++ (Clang 10.0.0) (judge verdict: Wrong Answer)

#include<iostream>
#include<vector>
#include<utility>

int main(){
  	static bool sieve[1000001];
  	long long n,p;
  	std::cin >> n >> p;
  	long long c = 2;
  	bool end = false;
  	long long nfact=0;
  	long long ans=1;
  	if(n==1){
      	std::cout << n << "\n";
      	return 0;
    }
  	while(p>1&&c<1000001&&!end){
      	nfact=0;
      	while(p%c==0){
          	nfact++;
          	p/=c;
        }
      	for(int i=0;i<((nfact-nfact%n)/n);i++){
          	ans*=c;
        }
      	for(int i=c*2;i<1000001;i+=c){
          	sieve[i] = true;
        }
      	for(int i=c+1;i<1000001;i++){
          	if(!sieve[i]){
              	c=i;
              	break;
            }
          	if(i==1000000)end=true;
        }
    }
  	std::cout << ans << "\n";
  	return 0;
}