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>
#include <algorithm>
#include <cmath>
using namespace std;

int main()
{
    long long int n, p, ans = 1;
    cin >> n >> p;
    long long int i = 1;
    long long int a = pow(2, n);
    long long int min = 2;
    int l = 2;
    if (n == 1)
    {
        cout << p << endl;
        return 0;
    }
    while (pow(i, n) <= p)
    {
        long long int tmp = pow(i, n);
        if (p % tmp == 0)
        {
            ans *= i;
            p /= tmp;
            if (i == 1)
                i++;
        }
        else
        {
            if (i == 3)
                i += 2;
            else if (i > 4)
            {
                i += l;
                l = 6 - l;
            }
            else
                i++;
        }
    }
    cout << ans << endl;
    return 0;
}