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;
using System.Collections.Generic;
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]);

        var alist = new List<int>();
        var ablist = new List<int>();
        for (int i = 1; i <= a; i++)
        {
            if (a % i == 0)
            {
                alist.Add(a / i);
            }
        }

        for (int i = 1; i <= b; i++)
        {
            if (b % i == 0 && alist.Contains(b / i))
            {
                ablist.Add(b / i);
            }
        }
        Console.WriteLine(ablist[k - 1]);

    }
}