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;
using LL = long long;
using PII = pair<int, int>;
#define FI(i,a,b) for(int i=(a);i<=(b);++i)
#define FD(i,b,a) for(int i=(b);i>=(a);--i)
#define DEBUG(x) cerr << #x << ": " << (x) << endl;
constexpr int inv(LL x, int m) { return x > m ? inv(x % m, m) : x > 1 ? inv(m % x, m) * (m - m / x) % m : x; }
constexpr int mpow(LL a, LL k, int m) { int r(1); for (a %= m; k; k >>= 1, a = a * a % m) if (k & 1)r = r * a % m; return r; }

int main() {
    LL n, p;
    cin >> n >> p;
    if (n == 1) cout << p << endl;
    else {
        LL ans = 1;
        for (LL i = 2;; i++) {
            LL x = 1;
            bool ok = true;
            for (LL j = 1; j <= n; j++) {
                x *= i;
                if (x > p) {
                    ok = false;
                    break;
                }
            }
            if (!ok) break;
            if (p % x == 0) ans = i;
        }
        cout << ans << endl;
    }
}