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: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;

class Program
{

    static void Main(string[] args)
    {
        var inputs = Console.ReadLine().Split(' ');
        var A = int.Parse(inputs[0]);
        var B = int.Parse(inputs[1]);
        var K = int.Parse(inputs[2]);

        var gcd = Gcd(A, B);
        var count = 0;
        var result = 0;
        for(int i = 1; i <= gcd; i++)
        {
            if ((A % i) * (B % i) == 0) count++;
            if(count == K)
            {
                result = i;
                break;
            }
        }

        Console.WriteLine(result);

    }

    /**
     * ユークリッド互除法
     * <see cref="https://qiita.com/gushwell/items/e9614b4ac2bea3fc6486"/>
     */
    public static long Gcd(long a, long b)
    {
        if (a < b)
            // 引数を入替えて自分を呼び出す
            return Gcd(b, a);
        while (b != 0)
        {
            var remainder = a % b;
            a = b;
            b = remainder;
        }
        return a;
    }
}