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.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;

namespace AtCoder
{
	public class Program
	{
		static void Main(string[] args)
		{

			int[] vs = Console.ReadLine().Split().Select(p => int.Parse(p)).ToArray();

			int a = vs[0];
			int b = vs[1];
			int k = vs[2];

			int c = 0;
			for (int i = a; i > 0; i--) {
				if (a % i == 0 && b % i == 0) {
					c++;
					if (c == k) {
						Console.WriteLine(i);
						return;
					}
				}
			}

		}
	}
}