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>
#define ll long long
using namespace std;

vector<pair<ll, ll>> prime_factorize(ll n){
    vector<pair<ll, ll>> res;
    for(ll p = 2; p * p <= n; p++){
        if(n % p != 0) continue;
        int num = 0;
        while(n % p == 0){ num++; n /= p;}
        res.push_back(make_pair(p, num));
    }
    if(n != 1) res.push_back(make_pair(n, 1));
    return res;
}

int main(){
    ll n, p;
    cin >> n >> p;
    auto v = prime_factorize(p);
    ll ans = 1;
    for(int i = 0; i < v.size(); i++){
        if(v[i].second / n == 0) continue;
        ans *= v[i].first * (v[i].second / n);
    }
    cout << ans << endl;
    return 0;
}