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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long N = sc.nextLong();
        long P = sc.nextLong();

        Map<Long, Integer> map = primeFactorization(P);

        long ans = map.entrySet()
                .stream()
                .filter(e -> e.getValue() >= N)
                .mapToLong(e -> e.getKey())
                .reduce(1, (a, b) -> a * b);

        System.out.println(ans);
    }

    private static Map<Long, Integer> primeFactorization(long n) {
        Map<Long, Integer> primeFactor = new HashMap<>();
        long m = n;
        int count = 0;
        while (m % 2 == 0) {
            count++;
            m = m / 2;
        }
        primeFactor.put(2L, count);

        for (int i = 1; i < m; i++) {
            count = 0;
            long a = 2 * i + 1;

            if (m % a != 0) {
                continue;
            }

            while (m % a == 0) {
                count++;
                m /= a;
            }
            primeFactor.put(a, count);
        }

        return primeFactor;
    }
}