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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define int long long
typedef pair<int, int> P;
int mod = 1e9+7;

vector<P> prime_factorize(int N){
	vector<P> ans;
	for(int a = 2; a*a <= N; a++){
		if(N%a == 0){
			int ex = 0;
			while(N%a == 0){
				ex++;
				N /= a;
			}
			ans.push_back(P(a, ex));
		}
	}
	if(N != 1) ans.push_back(P(N, 1));
	return ans;
}

signed main(){
	int N, Q; cin >> N >> Q;
	/*
	for(int i = 0; i < map.size(); i++){
        for(int j = 0; j < map[i].second/N; j++){
			 ans *= map[i].first;
		}
	} */
	vector<P> map = prime_factorize(Q);
    int ans = 1;
    for (auto p : map) {
        for (int j = 0; j < p.second/N; ++j) ans *= p.first;
    }
    cout << ans << endl;
}