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)

#define _LIBCPP_DEBUG 0
#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(int i=int(a);i<int(b);i++)
typedef vector<int> vi;
typedef long long ll;

bool ispri[1000010];

void eratos(ll n){
    rep(i,0,floor(sqrt(n)))ispri[i]=1;
    ispri[0]=0;ispri[1]=0;
    rep(i,2,floor(sqrt(n))){
        ll j=2*i;
        while(j<=floor(sqrt(n))){
            ispri[j]=0;
            j+=i;
        }
    }
}

int main(){
    ll N,P,an=1,cn;cin>>N>>P;
    if(N==1){
        cout<<P<<endl;
        return 0;
    }
    eratos(P);
    rep(i,2,floor(sqrt(P))){
        cn=0;
        if(ispri[i]){
            while(P!=1&&P%i==0){
                P=P/i;
                cn++;
            }
        }
        an=an*pow(i,(ll)(cn/N));
    }
    cout<<an<<endl;
        
    
}