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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        // Your code here! 
        Scanner sc = new Scanner(System.in);
        
        // n (10^12以下なら高速)
        long count = sc.nextLong();
        long n = sc.nextLong();
        
        // map: nの素因数の頻度 (60 => (2 -> 2, 3 -> 1, 5 -> 1)
        // list: nの素因数のリスト (60 => [2, 2, 3, 5])
        Map<Long, Integer> map = new HashMap<Long, Integer>();
        List<Long> list = new ArrayList<Long>();
        long m = n;
        for (long i = 2; (i * i) <= n; i++) {
            int cnt = 0;
            
            while ((m % i) == 0) {
                cnt++;
                m /= i;
                list.add(i);
            }
            
            if (cnt > 0) {
                map.put(i, cnt);
            }
        }
        if (m > 1) {
            map.put(m, 1);
            list.add(m);
        }
        
        long ans = 1;
        for (Long key : map.keySet()) {
            int val = map.get(key);
            if (val >= count) ans = ans * key * val;
        }
        System.out.println(ans);
    }
}