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 <bits/stdc++.h>
using namespace std;
using ll = long long;
#define forx(i, a, b) for (int i = (a); i < (b); i++)
#define rep(i, n) for (int i = 0; i < (n); i++)
vector<ll> a(1000100);
int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    ll n, p, ans = 1;
    cin >> n >> p;

    ll s = 2;

    while (p > 1 && s < 1000000)
    {
        if (p % s == 0)
        {
            a[s]++;
            p /= s;
        }
        else
            s++;
    }
    rep(i, 1000002)
    {
        if (n <= a[i])
            ans *= (a[i] / n) * i;
    }
    if(p!=1&&n==1)
        ans = p;

    cout << ans << endl;

    return 0;
}