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;
using System.Collections;
public class Program {
  public static void Main() {
    int[] line = ReadIntArray();
    int A = line[0], B = line[1], K = line[2];
    for (int i = Math.Min(A, B), j = 1; i > 0; i--) {
      if (A % i == 0 && B % i == 0) {
        if (j == K) {
          Console.WriteLine(i);
          return;
        } else {
          j++;
        }
      }
    }
  }

  private static string ReadStr() { return Console.ReadLine(); }
  private static int ReadInt() { return int.Parse(Console.ReadLine()); }
  private static double ReadDouble() { return double.Parse(Console.ReadLine()); }
  private static long ReadLong() { return long.Parse(Console.ReadLine()); }
  private static char ReadChar() { return Console.ReadLine()[0]; }
  private static string[] ReadStringArray() { return Console.ReadLine().Split(' '); }
  private static int[] ReadIntArray() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
  private static double[] ReadDoubleArray() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
  private static long[] ReadLongArray() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
  private static char[] ReadCharArray() { return Console.ReadLine().ToArray(); }
  private static string[] ReadCharStringArray() { return Console.ReadLine().ToCharArray().Select(c => c.ToString()).ToArray(); }
}