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: Runtime Error)

// https://beta.atcoder.jp/contests/abc115

#define SUBMIT

#include <bits/stdc++.h>

using namespace std;
using ui64 = uint64_t;

ui64 power(ui64 x, ui64 n) {
    ui64 res = 1;
    while (n != 0) {
        if (n % 2 == 1) res = (res * x);
        x = (x * x);
        n >>= 1;
    }
    return res;
}

int main() {
#ifdef SUBMIT
    auto& in = cin;
#else
    stringstream in(R"(1 1000
)");
#endif
    ui64 n, p;
    in >> n >> p;

    if (n == 1) {
        cout << p << endl;
        exit(0);
    }

    ui64 ans = 1;
    for (ui64 i = 1; i <= p; ++i) {
        auto y = power(i, n);
        if (p < y) break;
        if (p % y == 0) ans = i;
    }
    cout << ans << endl;
    return 0;
}