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 Map<Long,Long> map = new HashMap<>();
  public static List<Long> list = new ArrayList<>();
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    long N = sc.nextLong();
    long P = sc.nextLong();
    bunkai(P);
    long ans = 1;
    for(Long n : map.keySet()){
      //System.out.println(n + ":" + map.get(n));
      if(map.get(n) >= N){
        long tmp = map.get(n) / N;
        ans *= n * tmp;
      }
    }
    System.out.println(ans);
  }
  
  public static void bunkai(long n){
    while(n != 1){
      long num = sosuHantei(n);
      long count = 0;
      while(n % num == 0){
        count++;
        n /= num;
      }
      map.put(num, count);
    }
  }
  
  public static long sosuHantei(long n){
    for(long i = 2; i <= Math.sqrt(n); i++){
      if(n % i==0) return i;
    }
    return n;
  }
}