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)

object Main extends App{
  val sc = new java.util.Scanner(System.in)
  val A,B,K = sc.nextInt
  val isOK:(Int) => Boolean =(N)=>{
    A%N + B%N == 0
  }
  val OKlist = (100 until 0).filter(isOK)
  val OKList2 = List.tabulate(100){x:Int=>x+1}.filter(isOK)
  val ans = OKList2(OKList2.size-K)
  println(ans)
}