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.*;
import static java.lang.Math.*;
import java.math.BigInteger;

public class Main {
    
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		
		// 入力
		int a = sc.nextInt();
		int b = sc.nextInt();
		int k = sc.nextInt();
		
		// 計算
		int result = 0;
		int c = min(a, b);
		for(int i = c; i > 0; i--){
		    if(a%i == 0 && b%i == 0){
		        k--;
		        result = i;
		        if(k == 0) break;
		    }
		}

		// 出力
		System.out.println(result);
        
	}
}