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<bits/stdc++.h>
#define rep(i,n) for(ll i=0;i<n;++i)
#define rrep(i,n) for(int i=n-1;i>=0;--i)
#define yesno(flg) if(flg){cout<<"YES"<<endl;}else{cout<<"NO"<<endl;}
#define MAX_N 1002
#define i197 1000000007

using namespace std;

typedef long long ll;
typedef pair<ll,ll> P1;
typedef pair<int,int> Pi;
typedef pair<double,Pi> Pdi;
typedef pair<ll,int>Pli;
typedef pair<P1,ll> P2;
const ll INF=100000000000000001;
struct edge{int to,cost;};
int dy[]={0, 0, 1, -1};
int dx[]={1, -1, 0, 0};
struct Road{double cost;int a,b;};


int main() {

	ll n,p;

	cin>>n>>p;

	ll o=1;
	ll d=0;
	for(ll i=1; i<p+1; i++){
		d=1;
		for(ll j=1; j<n+1; j++){
			d*=i;
			if(d>p){
				break;
			}
		}
		if(d>p){
			break;
		}else{
			if(p%d==0){
				o=i;
			}
		}
	}
	cout<<o<<endl;
	return 0;
}