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 fr(i, n, m) for(int i = (n); i < (m); i ++)
#define pb push_back
#define pq priority_queue
#define st first
#define nd second

using namespace std;
typedef long long ll;
ll const inf = 1e9;
ll const mod = 998244353  ;

int main()
{
    ll n, p;
    cin >> n >> p;
    ll prime = 2;
    ll c = 0;
    ll gcd = 1;
    while(p > 1){
        if(p % prime == 0){
            c ++;
            p /= prime;
        }
        else{
            gcd = gcd * max(1LL, (c / n) * prime);
            c = 0;
            prime ++;
        }

    }
    if(c > 0) gcd = gcd * max(1LL, c / n * prime);
    cout << gcd << endl;

    return 0;

}