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{
  def main(args:Array[String]) = {
    val sc = new java.util.Scanner(System.in)
    val List(a,b,k) = List.fill(3)(sc.nextInt)
    val gcdAB = gcd(a,b)
    var divisor = 1
    var ans:Int = gcdAB
    var count = 0
    while(count != k){
      if(gcdAB % divisor == 0){
        count += 1
        ans = gcdAB / divisor
      }
      divisor += 1
    }
    
    println(ans)
    
  }
  
  def gcd(a:Int, b:Int) : Int = {
    if(a<b) gcd(b,a) else if(b==0) a else gcd(b,a%b)
  }
}