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 (2.13.1) (judge verdict: Wrong Answer)

import io.StdIn._

object Main extends App {
  val Seq(a, b, k) = readLine().split(" ").map(_.toInt).toSeq

  require(1 <= a && a <= 100)
  require(1 <= b && b <= 100)
  require(k >= 1)

  var i = 0
  var j = 0
  while (j != k) {
    i = i + 1
    if (a % i == 0 && b % i == 0) j = j + 1
  }

  println(i)
}