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;

public class MainClass
{
	public static void Main(string[] args)
	{
		string[] inputs = Console.ReadLine().Split(' ');
		int a = int.Parse(inputs[0]);
		int b = int.Parse(inputs[1]);
		int k = int.Parse(inputs[2]);
		int i = 1;
		if(Math.Max(a, b) == 1)
		{
			Console.WriteLine(1);
			return;
		}
		List<int> s = new List<int>(Math.Max(a,b));
		for( ; Math.Min(a,b) >= i;i++)
		{
			if(a % i == 0 && b % i == 0)
			{
				s.Add(i);
				
			}
		}
		Console.WriteLine(s[s.Count - k]);
	}
}