Problem:
Score : 200 points

Problem Statement

You are given positive integers A and B.

Find the K-th largest positive integer that divides both A and B.

The input guarantees that there exists such a number.

Constraints

All values in input are integers.

1 \leq A, B \leq 100

The K-th largest positive integer that divides both A and B exists.

K \geq 1

Input

Input is given from Standard Input in the following format:

A B K

Output

Print the K-th largest positive integer that divides both A and B.

Sample Input 1

8 12 2

Sample Output 1

2

Three positive integers divides both 8 and 12: 1, 2 and 4.
Among them, the second largest is 2.

Sample Input 2

100 50 4

Sample Output 2

5

Sample Input 3

1 1 1

Sample Output 3

1

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
      
      Scanner sc = new Scanner(System.in);
      
      int a = sc.nextInt();
      int b = sc.nextInt();
      int k = sc.nextInt();
      
      int c;
      
      if(b > a){
        c = a;
       	a = b;
       	b = c;
      }
      
      int count = 0;
      
      for(int i = 1; i <= b; i++){
        if(a % i == 0 && b % i == 0)
        count++;
      }
      
      System.out.println(count);
      
      int[]d = new int[count];
      int i;
      
      for(i = 0; i < count; i++){
        if(i == 0){
          d[i] = 1;
        } else {
          for(int l = d[i-1]+1; l <= b; l++){
            if(a % l == 0 && b % l == 0){
              d[i] = l;
              break;
        	} 
          }
        }
      }
      
     
     System.out.println(d[k-1]);
      
    }
}