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 <algorithm>
#include <array>
#include <cstddef>
#include <cstdint>
#include <iomanip>
#include <iostream>
#include <map>
#include <set>
#include <vector>

using namespace std;

int64_t pow_int(int64_t base, int64_t index)
{
    int64_t ans = 1;
    for (int i = 0; i < index; i++)
    {
        ans *= base;
    }
    return ans;
}

int main()
{
    int64_t n, p;
    cin >> n >> p;

    map<int64_t, int64_t> primes;
    int64_t p_tmp = p;
    for (int64_t p = 2; p_tmp != 1 && p * p <= p_tmp; p++)
    {
        while (p_tmp % p == 0)
        {
            primes[p] += 1;
            p_tmp /= p;
        }
    }
    if (p_tmp > 1)
    {
        primes[p_tmp] = 1;
    }

    int64_t ans = 1;
    for (auto p_c : primes)
    {
        if (p_c.second >= n)
        {
            ans *= pow_int(p_c.first, p_c.second / n);
        }
    }
    cout << ans << endl;
}