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 <bits/stdc++.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

using namespace std;
typedef long long int lli;

lli power(int x, lli n) {
    if (n == 0) return 1;

    if (n == 1) return x;

    if (n & 1) {
        lli t = power(x, n >> 1);
        return t * t * x;
    } else {
        lli t = power(x, n >> 1);
        return t * t;
    }
}

int main() {
    lli N, P;
    cin >> N >> P;

    if (N == 1) {
        cout << P << endl;
        return 0;
    }

    if (N >= 40) {
        cout << 1 << endl;
        return 0;
    }

    int ans = 0;
    for (int i = 1; true; i++) {
        lli t = power(i, N);
        if (t > P) break;
        if (P % t == 0) ans = i;
    }

    cout << ans << endl;
}