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 keyboard = new Scanner(System.in); 
		
		int A  = keyboard.nextInt();
		int B  = keyboard.nextInt();
		int K  = keyboard.nextInt();
		
		int N = A < B ? A : B;
		int[] ans = new int[N+1];
		
		for(int i=1; i<N+1; i++){
			int a = A % i;
			int b = B % i;
			if(a == 0 && b == 0){
				ans[i] = i;
			}
		}
		
		Arrays.sort(ans); 
		for(int j=N; j>=0; j--){
			if(N-j +1 == K){
				System.out.println(ans[j]) ;
				break;
			}
		}
		keyboard.close();	
	}
}