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 <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <numeric>
#include <cmath>
 
using namespace std;
using ll = long long;
 
int main(void){
    ll n,p;
    cin>>n>>p;
    vector<ll> c(sqrt(p)+2);
    ll ans = 1;
    for(ll i =2;i<sqrt(p)+2;++i){
        if(p%i == 0){
            while(p%i == 0){
               p /= i;
               c[i]++;
            }
            if(c[i] >= n) ans *= i * (c[i]/n);
        }
        
    }
    if(p > 1) ans *=p;
    cout << ans << endl;
}