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 Program
{
    static void Main()
    {
        var abk = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();

        var limit = Math.Min(abk[0], abk[1]);
        var nums = new List<int>();
        for (int i = 1; i <= limit; i++)
        {
            if (abk[0] % i == 0 && abk[1] % i == 0)
            {
                nums.Add(i);
            }
        }

        Console.WriteLine(nums[nums.Count - abk[2]]);
    }
}