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<climits>
#include<math.h>
#include<vector>
#include<algorithm>
#include<cstdio>
#include<stdio.h>
#include <string>
#include <complex>
#include <functional>
#include <map>
#include <queue>
using namespace std;
using ll = long long;
//typedef pair<string,string> P;
//double dat[100][100];
//int dp[6][1010];//動的計画法
//int prime[100001];
//char str[1010][1010];
//vector<pair<int,int> > pc[100001];
//int ABS(int a){return max(a,-a);}
int main(){
    ll n,p,ans=1;
    cin>>n>>p;
    if(n==1){
        cout<<p<<endl;
        return 0;
    }
    for(int i=1;i*i<=p;i++){
      	if(pow(i,n)>p) break;
        if(p%1!=0||(p%(int)pow(i,n)!=0)) continue;
        ans=i;
    }
    cout<<ans<<endl;
    return 0;
}