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 <bits/stdc++.h>
#ifdef _WIN32
#include "debug.hpp"
#endif
using namespace std;

#define rep(i,N) repf(i,0,N)
#define reps(i,N) repfs(i,1,N)
#define repf(i,a,b) for(int i=a;i<b;i++)
#define repfs(i,a,b) for(int i=a;i<=b;i++)
#define repr(i,N) for(int i=N-1;i>=0;i--)
#define reprs(i,N) for(int i=N;i>0;i--)
#define pb push_back

template<typename T> 
void chmax(T &a,T b){ a = max(a, b);};
template<typename T> 
void chmin(T &a,T b){ a = min(a, b);};

typedef long long ll;
typedef pair<int,int> P;
const int INF = 100000000;
const int MOD = 1000000007;
const int dx[9] = { 0, 1,  0, -1, 1,  1, -1, -1, 0};
const int dy[9] = { 1, 0, -1,  0, 1, -1, -1,  1, 0};
//--------------------------------------//
ll n,p;
map<ll,int> primes;
ll ans = 1;
void update(ll num){
	if(primes[num]==n){
		ans*=num;
	}
}
void factorize(ll num){
	bool is_roop=true;
	while(is_roop){
		is_roop=false;
		for(ll i=2;i*i<=num;i++)
			if(num%i==0){
				is_roop=true;
				num/=i;
				primes[i]++;
				update(i);
				break;
			}
	}
    primes[num]++;
	update(num);
}

void solve(){
	factorize(p);
	cout<<ans<<endl;
}

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	cin>>n>>p;
		solve();
	return 0;
}