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 B
{
    class Program
    {
        static void Main(string[] args)
        {
            int[] inputs = Console.ReadLine().Trim().Split(' ').Select(x => int.Parse(x)).ToArray();
            int n = inputs[0] <= inputs[1] ? inputs[0] : inputs[1];
            int m = inputs[0] > inputs[1] ? inputs[0] : inputs[1];

            var nd = GetDivisors(n);
            var md = GetDivisors(m);

            var ans = md.Reverse().Where(x => nd.Contains(x)).ElementAt(inputs[2] - 1);

            Console.WriteLine(ans);

#if DEBUG
            Console.ReadKey();
#endif
        }

        static IEnumerable<int> GetDivisors(int n)
        {
            for (int i = 1; i <= n; i++)
                if (n % i == 0)
                    yield return i;

            yield break;
        }
    }
}