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/ruby
# encoding: utf-8

A,B,$K = gets.split.map(&:to_i)

$taka = A
$aoki = B

def taka_ope
  if $taka.odd? then
    $taka -= 1
  end
  $aoki += $taka/2
  $taka = $taka/2
end

def aoki_ope 
  if $aoki.odd? then
    $aoki -= 1
  end
  $taka += $aoki/2
  $aoki = $aoki/2
end

if $K.even? then
  $K = $K/2
  $K.times do 
    taka_ope
    aoki_ope
  end
else
  $K = $K/2
  $K.times do 
    taka_ope
    aoki_ope
  end
  taka_ope
end

puts "#{$taka} #{$aoki}"