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)

/*package whatever //do not write package name here */

import java.io.*;
import java.util.*;

public class Main {
	public static void main (String[] args) {
		Scanner input = new Scanner(System.in);
		int a = input.nextInt();
		int b = input.nextInt();
		int k = input.nextInt();
		
		ArrayList<Integer> list = new ArrayList<>();
		ArrayList<Integer> lists = new ArrayList<>();
		
		for(int i=1;i<=a;i++)
		    if(a%i==0)
		        list.add(i);
		        
		for(int i=1;i<=b;i++)
		    if(b%i==0)
		        lists.add(i);
		        
		ArrayList<Integer> List = new ArrayList<>();
		
		for(int t:list)
		{
		    if(lists.contains(t))
		        List.add(t);
		}
		Collections.sort(List,Collections.reverseOrder());
		
		//System.out.println(List);
		System.out.println(List.get(k-1));
		
	}
}