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.Linq;
using System.Collections.Generic;
class c
{
    static void Main()
    {
        var abk = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int k = abk[2];
        var list = new List<int>();
        for (int i = 1; i <= Math.Min(abk[0], abk[1]); i++)
        {
            if (abk[0] % i == 0 && abk[1] % i == 0) list.Add(i);
        }
        Console.WriteLine(list[list.Count() - k]);
    }
}