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.*;
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();
    int cnt = 0;
    for(int i = Math.max(A,B); i>=1; i--){
      if(A%i == 0 && B%i==0){
        cnt++;
        if(cnt == K){
          System.out.println(i);
          break;
        }
      }
    }
  }
}