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)

#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <iomanip>
#include <stdio.h>
#include <numeric>
#include <math.h>
#include <algorithm>
#include <functional>
#include <cstring>
#include <array>
#include <vector>
#include <list>
#include <stack>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <deque>
#include <queue>
#include <complex>
#include <bitset>
#define full(c) c.begin(), c.end()
#define vector2d(name,type,h,w,init) vector<vector<type>> name(h,vector<type>(w,init)) 
const int PRIME = 1000000007;
const int INT_INF = 2147483647;
const long long int LL_INF = 9223372036854775807;
const double PI = acos(-1);
const double EPS = 0.0001;
typedef unsigned long long int ull;
typedef long long int ll;
using namespace std;

int main() {
	//cin.tie(0);
	//ios::sync_with_stdio(false);
	ll n, p, w = 1;
	cin >> n >> p;
	if (n == 1) {
		cout << p << endl;
		return 0;
	}
	map<ll, ll> ex;
	for (ll i = 2; i*i <= p; i++) {
		if (p%i == 0) {
			p /= i;
			ex[i] = 1;
			while (p%i == 0) p /= i, ex[i]++;
		}
	}
	ex[p] = 1;
	for (auto d : ex) {
		if (d.second >= n) w *= d.first;
	}
	cout << w << endl;
	return 0;
}