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>
#define REP(i, n) for(int i=0, i##_len=(n); i<i##_len; ++i)
using ll = long long;
using namespace std;

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

    unordered_map<long, long> counts;
    long maxi = powl(P, 1.0/(double)N);
    for (long i=2, tmp=P; tmp!=1 && i<=maxi;)
    {
        if (tmp % i == 0) { tmp /= i; ++counts[i]; }
        else ++i;
    }

    long ret = 1;
    for (auto& entry : counts)
    {
        long key = entry.first;
        long n = entry.second / N;
        if (n > 0) ret *= pow(key, n);
    }

    cout << ret << endl;

    return 0;
}