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<iostream>
#include<map>
using namespace std;
typedef long long ll;

int main(){
    int n;
    cin >> n;
    ll x;
    cin >> x;
    map<ll,int> m;
    for(ll i = 2; i*i <= x; i++){
        while(x%i == 0) m[i]++, x /= i;
    }
    if(x-1) m[x]++;
    ll ret = 1;
    for(auto p : m){
        ll val = p.first, tim = p.second;
        while(tim >= n){
            ret *= p.first;
            tim -= n;
        }
    }
    cout << ret << endl;
    return 0;
}