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 OCaml (4.02.3) (judge verdict: Accepted)

(* O(min {a, b}) *)
let solve a b k =
  let rec find acc n =
    if acc >= k then
      n + 1
    else
      find (if a mod n = 0 && b mod n = 0 then acc + 1 else acc) (n - 1)
  in
    find 0 (min a b)

let _ = Scanf.scanf "%d %d %d" (fun a b k -> solve a b k) |> string_of_int |> print_endline