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 {
  var get = readLine
  var a = get.split(" ")(0).toInt
  var b = get.split(" ")(1).toInt
  var c = get.split(" ")(2).toInt
  var sum = 0
  var loop = Math.max(a,b)
  var d = 0
  while(loop > 0) {
    if(a % loop == 0 && b % loop == 0){
      sum += 1
      if(sum == c)
		  d = loop
    }
    loop -= 1
  }
  println(d)
}