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 solve tak aoki k =
    let rec solve_t tak aoki k =
        if k = 0 then tak, aoki
        else solve_a (tak / 2) (aoki + tak / 2) (k - 1)
    and solve_a tak aoki k =
        if k = 0 then tak, aoki
        else solve_t (tak + aoki / 2) (aoki / 2) (k - 1)
    in solve_t tak aoki k

let () =
    let tak, aoki = Scanf.scanf "%d %d %d\n" solve in
    Printf.printf "%d %d\n" tak aoki