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.io.FileNotFoundException;
import java.io.FileReader;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) throws FileNotFoundException {

//    Scanner cin = new Scanner(new FileReader("input.txt"));
    Scanner cin = new Scanner(System.in);

    long n = cin.nextLong();
    long p = cin.nextLong();

    long root = (long)Math.pow(p,(double)1/n);
    //System.out.println(root);

    while (root >= 1) {
      long sq = (long)Math.pow(root,n);
      if (p%sq==0) {
        System.out.println(root);
        return;
      }
      else root--;
    }

  }

}