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 Ruby (2.3.3) (judge verdict: Accepted)

#! /usr/bin/env ruby

input = STDIN.read.chomp().split(" ").map{|i| i.to_i}

a = input[0]
b = input[1]
k = input[2]

def half_send(c)
  if c % 2 != 0 then
    c = c - 1
  end
  return c / 2
end

is_a_turn = true

while k > 0
  if is_a_turn then
    a = half_send(a)
    b = b + a
  else
    b = half_send(b)
    a = a + b
  end

  k = k - 1
  is_a_turn = !is_a_turn
end

puts sprintf("%s %s", a, b)