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 <bits/stdc++.h>
using namespace std;
typedef long long ll;

map<ll,int> facs;
void factor(ll i) {
    for (ll j = 2; j*j <= i; j++) {
        if (i % j == 0) {
            while (i % j == 0) {
                i /= j;
                facs[j]++;
            }
            factor(i);
            return;
        }
    }
    if (i > 1) {
        facs[i]++;
    }
}

ll expo(ll a, ll n) {
    ll res = 1;
    for (int i = 0; i < n; i++) {
        res *= a;
    }
    return res;
}

int main()
{
    ios_base::sync_with_stdio(false); cin.tie(NULL);
    ll N, P; cin >> N >> P;
    factor(P);
    ll ans = 1;
    for (auto p: facs) {
        ll r = p.second / N;        
        ans *= expo(p.first,r);
    }
    cout << ans << '\n';


    return 0;
}