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)

import java.util.Scanner

object Main {
  def main(args: Array[String]) = {
    val sc = new Scanner(System.in)
    val A, B, K = sc.nextInt()

    val min = A.min(B)
    val a = 1.until(min + 1).foldRight(List.empty[Int]) {
      (index, pre) =>
        if (A % index == 0 && B % index == 0) index :: pre else pre
    }
    println(a.reverse(K-1))
  }

}