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 Scala (2.11.7) (judge verdict: Accepted)

object Main {
  def main(args: Array[String]): Unit = {
    val nums            = io.StdIn.readLine().split(" ").map{_.toInt}
    val divide_max_num  = if(nums(0) < nums(1)) nums(0) else nums(1)
    var divisible_nums = Vector.empty[Int]

    (0 until divide_max_num).foreach { i =>
      val divide_num = divide_max_num - i
      if(nums(0)%divide_num == 0 &&
         nums(1)%divide_num == 0) {
        divisible_nums = divisible_nums :+ divide_num
      }
    }
    val print_number = nums(2) - 1
    if(print_number < 0) {
      println(1)
    }
    else {
      println(divisible_nums(print_number))
    }
  }
}