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.*;

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

    int A = sc.nextInt();
    int B = sc.nextInt();
    int K = sc.nextInt() - 1;

    List<Integer> divisorA = cul(A);
    List<Integer> divisorB = cul(B);

    List<Integer> common = new ArrayList<>();

    for(Integer a : divisorA){
      if(divisorB.contains(a)){
        common.add(a);
      }
    }

    Collections.sort(common, Collections.reverseOrder());

    System.out.println(common.get(K));

  }

  public static List<Integer> cul(int number) {
    List<Integer> divisor = new ArrayList<>();

    for (int i = 1; i <= number ; i++ ) {
      if (number%i == 0) {
        divisor.add(i);
      }
    }

    return divisor;
  }
}