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;

class Program
{
    static void Main(string[] args)
    {
        var inputs = ReadInts();
        var A = inputs[0];
        var B = inputs[1];
        var K = inputs[2];

        var ans = Enumerable.Range(1, Math.Min(A, B))
            .Select(n => Tuple.Create(n, A % n == 0 && B % n == 0))
            .Where(_ => _.Item2)
            .Reverse()
            .ElementAt(K - 1)
            .Item1;

        Console.WriteLine(ans);
    }


    public static string Read() { return Console.ReadLine(); }
    public static int ReadInt() { return int.Parse(Read()); }
    public static long ReadLong() { return long.Parse(Read()); }
    public static double ReadDouble() { return double.Parse(Read()); }

    public static string[] Reads() { return Console.ReadLine().Split(' '); }
    public static int[] ReadInts() { return Reads().Select(_ => int.Parse(_)).ToArray(); }
    public static long[] ReadLongs() { return Reads().Select(_ => long.Parse(_)).ToArray(); }
    public static double[] ReadDoubles() { return Reads().Select(_ => double.Parse(_)).ToArray(); }
}