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: Runtime Error)

#include <iostream>
#include <vector>
#include <map>
using namespace std;

int main(int argc, char const *argv[])
{
    long long N, P, i, j, P_, tmp[10001];
    for (i = 1; i <= 10001; i++)
    {
        tmp[i] = 0;
    }
    cin >> N >> P;
    for (i = P, P_ = 2; i >= P_; P_++)
    {
        for (j = 0; i % P_ == 0; j++)
        {
            i /= P_;
        }
        if (j == 0)
        {
            continue;
        }
        //        cout << P_ << " " << j << endl;
        tmp[P_] = j;
    }

    long long ans = 1;

    for (i = 1; i <= 10000; i++)
    {
        if (tmp[i] >= N)
        {
            ans *= i;
        }
    }

    cout << ans << endl;

    return 0;
}