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();

   if(B>A)
   {
    int s =B;
    B = A;
    A = s;
   }
   
   int count =0;
   int ans=0;
   int cd = B;
   while(count<K)
   {
     if(A%cd==0) 
     {
       count++;
       ans = cd;
     }
     cd--;
   }
   System.out.println(ans);
 }
}