Problem:
Score : 400 points

Problem Statement

Takahashi is going to buy N items one by one.

The price of the i-th item he buys is A_i yen (the currency of Japan).

He has M discount tickets, and he can use any number of them when buying an item.

If Y tickets are used when buying an item priced X yen, he can get the item for \frac{X}{2^Y} (rounded down to the nearest integer) yen.

What is the minimum amount of money required to buy all the items?

Constraints

All values in input are integers.

1 \leq N, M \leq 10^5

1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 ... A_N

Output

Print the minimum amount of money required to buy all the items.

Sample Input 1

3 3
2 13 8

Sample Output 1

9

We can buy all the items for 9 yen, as follows:

Buy the 1-st item for 2 yen without tickets.

Buy the 2-nd item for 3 yen with 2 tickets.

Buy the 3-rd item for 4 yen with 1 ticket.

Sample Input 2

4 4
1 9 3 5

Sample Output 2

6

Sample Input 3

1 100000
1000000000

Sample Output 3

0

We can buy the item priced 1000000000 yen for 0 yen with 100000 tickets.

Sample Input 4

10 1
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 4

9500000000

Solution in Fortran (gfortran v4.8.4) (judge verdict: Time Limit Exceeded)

      program answer
      implicit none
      integer(8) N,M
      integer(8),allocatable,dimension(:) :: A
      double precision,allocatable,dimension(:) :: B
      double precision :: tmp
      integer(8) :: i,j,res
      intrinsic dble,maxval
      res = 0
      read(*,*) N,M
      allocate(A(N),B(N))
      read(*,*) (A(i),i=1,N)
      do i=1,N
        B(i) = dble(A(i))
      end do
      do i=1,M
        tmp = maxval(B)
      lp:do j=1,N
          if( tmp == B(j)) then
            B(j) = tmp/2.0d0
            exit lp
          end if
        end do lp
      end do
      do i=1,N
        A(i) = B(i) + 0.0
        res = res + A(i)
      end do
      write(*,'(I0)') res
      end program answer