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: Accepted)

import java.util.*;

class A {
    static final int S = 1_000_000;

    public static void main(String... args) {
        final Scanner sc = new Scanner(System.in);
        final long N = sc.nextLong();
        final long P = sc.nextLong();
        final boolean[] notPrime = new boolean[S + 1];
        for (int i = 2; i * i <= S; i++)
            if (!notPrime[i])
                for (int j = i * i; j <= S; j += i)
                    notPrime[j] = true;
        final List<Integer> primes = new ArrayList<>();
        for (int i = 2; i <= S; i++)
            if (!notPrime[i])
                primes.add(i);
        final Map<Long, Integer> map = new HashMap<>();
        long l = P;
        for (final int prime : primes)
            if (l % prime == 0) {
                int power = 0;
                while (l % prime == 0) {
                    power++;
                    l /= prime;
                }
                map.put((long) prime, power);
            }
        if (l > 0)
            map.put(l, 1);
        long ans = 1l;
        for (final long prime : map.keySet())
            for (int i = 0; i < map.get(prime) / N; i++)
                ans *= prime;
        System.out.println(ans);
    }
}
public class Main {
    public static void main(String...args) {
        A.main();
    }
}