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 () =
  Scanf.scanf "%d %d %d" @@ fun a b k ->
  let rec f c i =
    if c = k then i+1
    else if a mod i = 0 && b mod i = 0 then f (c+1) (i-1)
    else f c (i-1)
  in f 0 (min a b) |> Printf.printf "%d\n"