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.Linq;

public class Program
{
	//limit
	static int A, B, C, N;

	static int[] l;

	public static void Main(string[] args)
	{
		// スペース区切りの整数の入力
		var input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();

		var A = input[0] * 100;
		var B = input[1] * 100;
		var K = input[2];

		var answer = 0;
		var flag = true;
		var counter = 0;
		while (flag)
		{
			answer++;
			Double test = 50 % 4;
			if (A % answer == 0 & B % answer == 0)
			{
				counter++;
				if (counter == K)
					flag = false;
			}
		}

		Console.WriteLine(answer);
	}
}