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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.*;
import java.lang.*;

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 i = -1;
        if(a>b){
            i = b;
        }else{
            i = a;
        }
        int count = 0;
        while(true){
            if(a%i==0&&b%i==0){
                count++;
            }
            if(count == k){break;}
            i--;
        }
        System.out.println(i);
        sc.close();
    }
}