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: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using System.ComponentModel;
using System.Linq;
using System.Threading.Tasks;
class Program
{
	static void Main(string[] args)
	{
		string[] input = Console.ReadLine().Split(' ');
		int a = int.Parse(input[0]);
		int b = int.Parse(input[1]);
		int k = int.Parse(input[2]);
		int cnt = 0;
		int r = a;
		if (a > b) { r = b; }
		while (cnt < k)
		{
			if (a % r == 0 && b % r == 0)
			{
				cnt++;
			}
			r--;
		}
		Console.WriteLine(r);
	}
}