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 extends App {
  var input = scala.io.StdIn.readLine()
  val abkArray =  input.split(" ").map(_.toInt)
  val a = abkArray(0)
  val b = abkArray(1)
  val k = abkArray(2)
  var i = 1
  var s = 1
  var array = Vector.empty[Int]

  while (s <= a && s <= b)  {
    if (a % s == 0 && b % s == 0) {
      array :+= s
    }
    s += 1
  }
  val arrayr = array.reverse
  print(arrayr.apply(k - 1))
}