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 <string>
#include <algorithm> 
#include <cstdlib>
#include <map>
#include <queue>
#include <vector>
#include <cmath>
#include <limits>
#define ll long long
using namespace std;
int main(){
    ll N,P,h;
    cin >> N >> P;
    ll a=P;
    ll count=0,ans=-1,answer=1;
    for(ll i=2;i<1000005;i++){
        while(1){
            if(P%i==0){
                P = P / i;
                count++;
            }else{
                break;
            }
        }
        if(count>=N){
            answer = i * answer;
        }
        count=0;
    }
    if(N==1){
        cout << a << endl;
    }else if(a==1){
        cout << 1 << endl;
    }else{
        cout << answer << endl;
    }
}