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: Time Limit Exceeded)


#include<iostream>
#include<string>
#include<cstdio>
#include<algorithm>
#include<cstdlib>
#include<cmath>
#include<vector>
#include<utility>
#include<queue>
#include<stack>
#include<set>
#include<map>
#include<unordered_set>
#include<unordered_map>
#include<bitset>
using namespace std;
#define INF 2147483647
//#define MODE 1
#ifdef MODE
#define DEB(X) cout<< #X <<": "<<X<<" ";
#define ARDEB(i,X) cout<< #X <<"["<<i<<"]: "<<X[i]<<" ";
#define END cout<<endl;
#else
#define DEB(X) {}
#define ARDEB(i,X) {}
#define END {}
#endif
typedef long long int ll;

vector<int> prime;
unordered_map<int,int> prco;
void prfac(ll n){
	int a=2;
	while(n>=a*a){
		if(n%a==0){
			//prime.push_back(a);
			n/=a;
			prco[a]++;
		}
		else{
			a++;
		}
	}
	//prime.push_back(n);
	prco[n]++;
}

int main(){
    
    ll n,p;
    cin>>n>>p;
    if(p==1){
        cout<<1<<endl;
        return 0;
    }
    if(n==1){
        cout<<p<<endl;
        return 0;
    }
    prfac(p);
    ll ans=1;
    for(auto x:prco){
        while(x.second-n>=0){
            x.second-=n;
            ans*=x.first;
        }
    }
    cout<<ans<<endl;
    
}