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 <iostream>
#include <vector>
#include <stack>
#include <queue>
#include <algorithm>
#include <cstdlib>
#include <cmath>
#include <numeric>

using namespace std;

#define rep(i, n) for(int i = 0; i < n; i++)
#define repi(i, start, end) for(int i = start; i < end; i++)
#define all(x) (x).begin(), (x).end()
#define debug(x) cout << (x) << endl;
typedef long long ll;
const int MAX = 999999999;

int main(){
    ll n, p;
    cin >> n >> p;

    vector<int> div_nums;
    repi(i, 1, pow(p, 1.0/n)+1) if(p % i == 0) div_nums.push_back(i);

    int max_val = -1;
    rep(i, div_nums.size()){
        double tmp = pow(p * 1.0 / div_nums[i], 1.0/n);
        if(tmp - (int)(tmp) == 0) max_val = max(max_val, div_nums[i]);
    }

    if(p == max_val){
        cout << p << endl;
        return 0;
    }

    int dived_p = p / max_val;
    cout << (int)(pow(dived_p, 1.0/n)) << endl;
}