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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.Scanner

fun main(args: Array<String>) {
  val scanner = Scanner(System.`in`)
  val A = scanner.nextInt()
  val B = scanner.nextInt()
  var K = scanner.nextInt()
  scanner.close()
  for (i in 100 downTo 1) {
    if (A % i == 0 && B % i == 0) {
      K--
      if (K == 0) {
        print(i)
        return
      }
    }
  }
}