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.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;

namespace AtCoder
{
    class Program
    {
        static void Main()
        {
            var raw = ReadLine().Split().Select(int.Parse).ToArray();
            var A = raw[0];
            var B = raw[1];
            var K = raw[2];

            var c = 0;
            for (int i = Math.Max(A, B); i > 0; i--)
            {
                if (A % i == 0 && B % i == 0) c++;
                if (c == K)
                {
                    WriteLine(i);
                    break;
                }
            }
        }
    }
}