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>
#define REP(i, n) for(int i = 0; i < n; i++)
#define REPR(i, n) for(int i = n; i >= 0; i--)
#define FOR(i, m, n) for(int i = m; i < n; i++)
#define INF 2e9
#define ALL(v) (v).begin(), (v).end()
using namespace std;
typedef long long ll;
int GCD(int a,int b){return b?GCD(b,a%b):a;}
int LCM(int a,int b){return (a*b)/GCD(a,b);}
int abs(int x){return x>0?x:-x;}
 
//const int dx[] = {1, 0, -1, 0, 1, -1, -1, 1};
//const int dy[] = {0, 1, 0, -1, 1, 1, -1, -1};

int main()
{
	ll n, p;
	cin >> n >> p;
	map<int, int> mp;
	int ans = 1;

	if (n == 1){
		cout << p << endl;
		return 0;
	}

	for (int i = 2; i*i <= p; i++){
		if (p % i == 0){
			while (1){
				if (p % i != 0 or p == 0) break;
				p /= i;
				mp[i]++;
			}
		}
	}

	for (auto itr = mp.begin(); itr != mp.end(); itr++){
		if (itr->second >= n) ans *= itr->first;
	}

	cout << ans << endl;

}