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>

using namespace std;

int main() {
    long long n, p;
    cin >> n >> p;

    long long ans = 1;
    for (int i = 2; 1ll * i * i <= p; i++){
        if (p % i == 0) {
            int c = 0;
            while (p % i == 0) {
                c++;
                p /= i;
            }

            for (int j = 0; j < c / n; j++) {
                ans *= i;
            }
        }
    }

    if (n == 1) {
        ans *= p;
    }

    cout << ans << endl;

    return 0;
}