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 System.Threading.Tasks;

namespace ABC120 {
	class ABC120_B {
		static void Main(string[] args) {
			var input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
			var A = input[0];
			var B = input[1];
			var K = input[2];

			var loop = A > B ? B : A;
			var div = new List<int>();
			for (int i = 1; i <= loop; i++) {
				if (A % i != 0) {
					continue;
				}
				if (B % i != 0) {
					continue;
				}
				div.Add(i);
			}
			div.Reverse();
			Console.WriteLine(div.Take(K).Last());
		}
	}
}