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 {
  val sc = new Scanner(System.in)
  def main(args: Array[String]): Unit = {
    val a = sc.nextInt
    val b = sc.nextInt
    val k = sc.nextInt

    val d = gcd(a,b)
    val r = (d to 1 by -1).filter(d % _ == 0)(k - 1)

    println(r)
  }

  def gcd(a: Int , b: Int): Int ={
    if(b == 0) a
    else
    if(a < b) gcd(b,a)
    else gcd(a % b,b)
  }

}