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: Runtime Error)

#include <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>
#include <string>
#include <deque>
#include <cmath>
#include <queue>
#include <ctime>
#include <functional> // std::greater <int> ()
#define inf 1000000000000000001

typedef long long ll;
typedef long double ld;
using namespace std;

//variables
ll n, p, ans=1;
ll prime[1000001], dem[1000001];
int pos=0;
bool check=0;

//functions
void factor(ll x){
	ll n=2;
	while(x!=1){
		if(x%n==0){
			pos++;
			prime[pos]=n;
			while(x%n==0){
				x=x/n;
				dem[pos]++;
			}
		}
		if(n*n>x){
			pos++;
			prime[pos]=x;
			dem[pos]=1;
		}
		n++;
	}
}

void input(){
	cin >> n >> p;
}

void solve(){
	ll temp;
	if(n==1){
		check=1;
		return;
	}
	factor(p);
	for(int i=1; i<=pos; i++){
		temp=dem[i]/n;
		for(ll j=1; j<=temp; j++){
			ans*=prime[i];
		}
	}
}

void output(){
	if(check){
		cout << p;
		return;
	}
	cout << ans;
	return;
}

int main(){
//  freopen(".INP", "r", stdin);
//  freopen(".OUT", "w", stdout);
	input();
	solve();
	output();
	return 0;
}
//  Author: NamSPro