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.Collections.Generic;
using System.Linq;
using System.Numerics;
class Program
{       
    public void Slove()
    {
        var inputs = Console.ReadLine().Split();
        int a = int.Parse(inputs[0]);
        int b = int.Parse(inputs[1]);
        int k = int.Parse(inputs[2]);
        int max = Math.Max(a, b);
        int result = Enumerable.Range(1, max).Where(x => a % x == 0 && b % x == 0).ToArray()[k - 1];
        System.Console.WriteLine(result);
    }
    
    static void Main(string[] args)
    {
        new Program().Slove();
    }
}