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 <cmath>
#include <iostream>
#include <map>
using namespace std;
typedef long long ll;

map<ll, ll> prime_fac(ll A)
{
    map<ll, ll> mp{};

    ll root_A = pow(A, 0.5);
    for (ll d = 2; d <= root_A; d++)
    {
        while (A % d == 0)
        {
            mp[d]++;
            A /= d;
        }

        if (A == 1) break;
    }

    if (A != 1) mp[A]++;

    return mp;
}

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

    map<ll, ll> pf = prime_fac(P);

    ll ans = 1;
    for (auto k : pf)
    {
        ll p = k.first, e = k.second;
        if (e >= N) ans *= pow(p, e / N);
    }

    cout << ans << endl;
    return 0;
}