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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program exchange
  implicit none
  integer :: a, b, k, i
  read(*,*) a, b, k
  do i = 1, k
    a = (a-mod(a,2))/2
    b = b+a
    call swap(a,b)
  end do
  if (mod(k,2) == 1) call swap(a,b)
  write(*,'(i0,x,i0)') a, b
contains
  subroutine swap(a,b)
    integer, intent(inout) :: a, b
    a = xor(a,b)
    b = xor(a,b)
    a = xor(a,b)
  end
end program exchange