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: Accepted)

import java.util.*;
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 ans=0;
  for(int i=100;i>0;i--){
  	if(a%i==0&&b%i==0){
    ans++;
    }
    if(ans==k){System.out.println(i);
              break;
              }
  }
}
}