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 read() = {
    val sc = new Scanner(System.in)
    val a = sc.nextInt()
    val b = sc.nextInt()
    val k = sc.nextInt()
    (a, b, k)
  }


  def solve(a: Int, b: Int, k: Int)= {
    def isDevidedByAandB(n:Int) = a%n ==0 && b%n==0

    val cmList = (1 to 100).filter(isDevidedByAandB) // 小さい順で並んだaとbの公約数
    cmList.reverse(k-1)
  }


  def main(args: Array[String]): Unit = {
    val (a, b, k) = read()
    println(solve(a, b, k))
  }
}