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)

//2019/3/12
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();

		int ans = 0;

		int i = 0;

		if(A<B) {

			for(int j=A;i<K;j--) {

				if(A%j==0 && B%j==0) {

					i++;

					ans = j;
				}
			}
		}else {

			for(int j=B;i<K;j--) {

				if(A%j==0 && B%j==0) {

					i++;

					ans = j;
				}
			}
		}
		System.out.println(ans);
	}

}