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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;


public class B
{
	public static void Main()
	{
		string[] args = Console.ReadLine().Split(' ');
		int A = Int32.Parse(args[0]);
		int B = Int32.Parse(args[1]);
		int K = Int32.Parse(args[2]);

		int ans = Math.Max(A,B) + 1;
		int counter = 0;
		while(counter < K)
		{
			ans--;
			if((A % ans == 0) && (B % ans == 0))
				counter++;
		}
			
		Console.WriteLine(ans);
	}	
}