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)

let calc a b =
  let rec iter i =
    if i == 0 then
      []
    else if a mod i == 0 && b mod i == 0 then
      i :: iter (i - 1)
    else iter (i - 1)
  in iter 100
let () =
  let (a, b, k) = Scanf.scanf "%d %d %d" (fun a b k -> (a, b, k)) in
  let l = calc a b in
  (*List.iter (fun e -> e |> string_of_int |> print_endline) l*)
  List.nth l (k - 1) |> string_of_int |> print_endline