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;

namespace ForAtcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            long[] inputLongArray = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();
            var a = inputLongArray[0];
            var b = inputLongArray[1];
            var k = (int)inputLongArray[2];
            var alist = new List<long> { };
            for (var i = a + b; i > 0; i--)
            {
                if (a % i == 0 && b % i == 0) alist.Add(i);
            }
            Console.WriteLine(alist[k-1]);
        }
    }
}