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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);

    long N = scanner.nextLong();
    long P = scanner.nextLong();

    if (N == 1) {
      System.out.println(P);
      return;
    }
    int[] primes = primes(1_000_000);
    long max = 1;
    for (int p : primes) {
      long count = 0;
      while (P % p == 0) {
        P /= p;
        count++;
      }
      if (count >= N) max *= p * (count / N);
    }
    System.out.println(max);
  }

  public static int[] primes(int n) {
    boolean[] isNotPrime = new boolean[n + 1];
    isNotPrime[0] = isNotPrime[1] = true;
    for (int i = 2; i < Math.sqrt(n); i++) {
      if (!isNotPrime[i]) {
        for (int j = 2; i * j <= n; j++) {
          isNotPrime[i * j] = true;
        }
      }
    }
    final List<Integer> ls = new ArrayList<>();
    for (int i = 2; i <= n; i++) if (!isNotPrime[i]) ls.add(i);
    int[] res = new int[ls.size()];
    for (int i = 0; i < ls.size(); i++) res[i] = ls.get(i);
    return res;
  }
}