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 <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <queue>
#include <cmath>
#include <set>
typedef long long ll;
typedef unsigned int uint;
using namespace std;

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

    ll n, p, ans=1LL;
    cin >> n >> p;
    ll d = 2LL;
    if (n >= 40) {
        cout << 1 << endl;
        return 0;
    } else if (n == 1) {
        cout << p << endl;
        return 0; 
    }
    
    while (p > 1) {
        ll count = 0LL;
        while(p % d == 0) {
            count += 1LL;
            p /= d;
        }
        if (count >= n) {
            ans *= d * (count / n);
        }
        d += 1LL;
        if (d > 1000000LL) {
            break;
        }
    }

    cout << ans << "\n";
    return 0;
}