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: Time Limit Exceeded)

import java.util.*;
import java.io.*;

public class Main {

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

    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    
    String[] in = br.readLine().split(" ");
    long n = Long.parseLong(in[0]);
    long p = Long.parseLong(in[1]);

    br.close();

    Map<Long, Integer> prime = new HashMap<>();

    for(long i = 2; p > 1; i++){
      int cnt = 0;
      while(p % i == 0){
        p /= i;
        cnt++;
      }
      if(cnt > 0){
        prime.put(i, cnt);
      }
    }

    long ans = 1;

    for(Map.Entry<Long, Integer> e : prime.entrySet()){
      int t = e.getValue();
      while(t >= n){
        ans *= e.getKey();
        t -= n;
      }
    }

    System.out.println(ans);
  }
}