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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;
import java.util.ArrayList;

public class Main {
  public static void main (String[] args) {
    Scanner in = new Scanner(System.in);

    while (in.hasNext()) {
      int A = in.nextInt();
      int B = in.nextInt();
      int K = in.nextInt();

      ArrayList<Integer> commonDivisor = new ArrayList<Integer>();

      for (int i = 1; i <= 100; ++i) {
        if (A % i == 0 && B % i == 0) {
          commonDivisor.add(i);
        } 
      }

      System.out.println(commonDivisor.get(commonDivisor.size() - K));
    }
  }
}