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;
using System.IO;


class Program
{
    public static long Read()
    {
        return long.Parse(Console.ReadLine());
    }

    public static long[] Reads()
    {
        return Console.ReadLine().Split().Select(long.Parse).ToArray();
    }


    public static void Main()
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);

        var input = Reads();
        var a = input[0];
        var b = input[1];
        var k = input[2];
        if (a < b)
        {
            long tmp = b;
            b = a;
            a = tmp;
        }
        var x = new List<long>();
        for(long i = b; i >= 1; i--)
        {
            if (a % i == 0 && b % i == 0)
            {
                x.Add(i);
            }
        }
        Console.WriteLine(x[(int)k - 1]);



        Console.Out.Flush();
    }
}