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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define INF 1LL<<62
#define inf 1000000007


map<ll,ll>a;
int main() {
	ll n,k;
	cin>>n>>k;
	if(n==1){
		cout << k;
		return 0;
	}
	for(int i=2;i*i<=k;i++){
		while(k%i==0){
			a[i]++;
			k=k/i;
		}
	}
	ll ans=1;
    for(auto itr = a.begin(); itr != a.end(); ++itr) {
        ll val=itr->second;
        ll key=itr->first;
        if(val>=n){
        	ans*=val/n*key;
        }
    }
	cout <<ans;
	return 0;
}