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): Seq[Int] = readLine().split(" ").map(_.toInt)
 
  var x = 1
  var y = 0
  var z = 0
  while(y < k) { 
   	if(a%x==0 && b%x==0){
      y += 1
      z = x
    }
    x += 1
  }
  println(z)
}