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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

/*

k ^ n | n

*/
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
# define int long long
using namespace std ;

int n , m , Ans ;
inline int Fpw(int Base , int k) {
	int temp = 1 ;
	while(k) {
		if(k & 1) temp = temp * Base ;
		Base = Base * Base ; k >>= 1 ;
	    if(temp > m || temp < 0) return -1 ;
	}
	return temp ;
}
# undef int
int main() {
# define int long long
    cin >> n >> m ;
	if(n == 1) {
		cout << m << endl ;
		return 0 ;
	}
	int prex = 0 ;
	int upp = pow(m , 1.0 / n) ;
	for(int i = 1 , x ; prex <= m ; i ++) {
		prex = Fpw(i , n) ;
		if(prex <= 0) break ;
		if(m % prex == 0) Ans = i ;
	}
	cout << Ans << endl ;
	return 0 ;
}