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;

class Main{
  public static void main(String args[]){
    Scanner scan = new Scanner(System.in);

    int a = scan.nextInt();
    int b = scan.nextInt();
    int k = scan.nextInt();

    int d = 1;
    int c = 0;
    while(true) {
    	if(a%d==0 && b%d==0) {
    		c++;
    		if(k==c) {
    			break;
    		}
    	}
    	d++;
    }
    System.out.println(d);
  }
}