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 in = scala.io.Source.stdin.getLines.toSeq
  val ls = in.map(_.split(' ').map(_.toInt).toIndexedSeq).head
  val A = ls(0)
  val B = ls(1)
  val K = ls(2)
  var count = 0
  var i=Math.min(A,B)
  while(count<K){
    if(A%i==0 && B%i==0) count+=1
    i-=1
  }
  val ret = i+1
  println(ret)
}