Problem:
Score : 200 points

Problem Statement

In the beginning, Takahashi has A cookies, and Aoki has B cookies.
They will perform the following operation alternately, starting from Takahashi:

If the number of cookies in his hand is odd, eat one of those cookies; if the number is even, do nothing. Then, give one-half of the cookies in his hand to the other person.

Find the numbers of cookies Takahashi and Aoki respectively have after performing K operations in total.

Constraints

1 \leq A,B \leq 10^9

1 \leq K \leq 100

A,B and K are integers.

Input

Input is given from Standard Input in the following format:

A B K

Output

Print the number of cookies Takahashi has, and the number of cookies Aoki has, in this order, after performing K operations in total.

Sample Input 1

5 4 2

Sample Output 1

5 3

The process will go as follows:

In the beginning, Takahashi and Aoki have 5 and 4 cookies, respectively.

Takahashi eats one cookie and gives two cookies to Aoki. They now have 2 and 6 cookies, respectively.

Aoki gives three cookies to Takahashi. They now have 5 and 3 cookies, respectively.

Sample Input 2

3 3 3

Sample Output 2

1 3

Sample Input 3

314159265 358979323 84

Sample Output 3

448759046 224379523

Solution in OCaml (4.02.3) (judge verdict: Accepted)

let a, b, k = Scanf.scanf " %d %d %d" @@ fun a b c -> a, b, c
let ns = [|a; b|]
let _ =
  for i = 0 to k - 1 do
    let r = i mod 2 in
    if ns.(r) mod 2 = 1 then ns.(r) <- ns.(r) - 1; ns.(1 - r) <- ns.(1 - r) + ns.(r) / 2; ns.(r) <- ns.(r) / 2 done;
  Printf.printf "%d %d\n" ns.(0) ns.(1)