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 scala.io.StdIn.readLine

object Main extends App {
  val Array(a, b, k) = readLine().split(' ').map(_.toInt)
  
  val aDivisors = (1 to a).filter(x => a % x == 0).toSet
  val bDivisors = (1 to b).filter(x => b % x == 0).toSet
  val commonDivisors = aDivisors.intersect(bDivisors).toSeq.sorted
  println(commonDivisors(k - 1))
}