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)

#include<bits/stdc++.h>
using namespace std;
using ll = long long;

template<typename A, size_t N, typename T>
void Fill(A (&array)[N], const T &val){
    std::fill( (T*)array, (T*)(array+N), val );
}

int main(){
    ll N,P,end;
    cin >> N >> P;
    ll A[20000000];
    Fill( A, (long long)0 );
    end = 1;
    for(ll i = 2;i*i <= P;i++){
        while(P % i == 0){
            A[i]++;
            P /= i;
            end = i;
        }
    }
    if(P != 1) {
        A[P] = 1;
        end = P;
    }
    ll ite = 1;
    int ts;
    for(ll i = 2;i <= end;i++){
        ts = A[i] / N;
        if(ts != 0)
            ite *= pow(i,ts);
    }
        
    cout << ite << "\n";
    return 0;
}