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<algorithm>
#include<complex>
#include<ctype.h>
#include<iomanip>
#include<iostream>
#include<map>
#include<math.h>
#include<numeric>
#include<queue>
#include<set>
#include<stack>
#include<stdio.h>
#include<string>
#include<string>
#include<vector>

using namespace std;
typedef long long ll;

#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define ALL(v) (v).begin(), (v).end()
#define p(s) cout<<(s)<<endl
#define p2(s, t) cout << (s) << " " << (t) << endl
#define pn(s) cout << (#s) << " " << (s) << endl

const ll mod = 1e9 + 7;
const ll inf = 1e18;

ll mypow(ll a, ll b, ll threshold){
    ll ans = 1;
    FOR(i, 0, b){
        ans *= a;
        if(ans > threshold){
            return -1;
        }
    }
    return ans;
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);

    // input
    ll N, P;
    cin >> N >> P;

    ll answer = 1;
        
    FOR(i, 2, inf){
        ll div = mypow(i, N, P);
        if(div == -1){
            break;
        }

        if(P % div == 0){
            answer *= i;  
            P /= div;
        }
    }

    p(answer);

    return 0;
}