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 main
  
  implicit none ! 02;01
  integer :: n, m
  integer, allocatable :: a(:)
  integer :: i,j, tmp, tmpo
  integer(8) :: money
  
  read(*,*) n,m
  allocate( a(n) )
  read(*,*) a
  
  call quick_sort( a, 1, n ) 

  do j = 1, m
    a(maxloc( a )) = a(maxloc( a )) / 2 
  end do
  money = 0
  do i = 1, n
    money = money + int( a(i), kind = 8 )
  end do
  print*, money

end program main

recursive subroutine quick_sort( a, i, j )

  implicit none
  integer, intent(in) :: i,j
  integer, intent(inout) :: a(i:j)
  integer :: p, pl, k, tmp

  if( i == j ) return
 
  p  = pivot(a,i,j)
 
  if( p /= -1 ) then
    call partition(a(i:j),i,j,a(p),k)
    call quick_sort(a(i:k-p),i,k-1)
    call quick_sort(a(k:j),k,j)
  end if

contains 

subroutine partition( a, i, j, x, l ) 
  
  implicit none
  integer, intent(in) :: i,j,x
  integer, intent(inout) :: a(i:j)
  integer, intent(out) :: l
  integer :: r, t
   
  l = i 
  r = j 

  do while( l<=r )
    do while( l<=j .and. a(l) <  x ) 
      l = l+1
    end do
    do while( r> i .and. a(r) >= x ) 
      r = r-1
    end do
    if(l>r) exit
    t = a(l)
    a(l) = a(r)
    a(r) = t
    l = l+1
    r = r-1
  end do
  
end subroutine partition

function pivot( a, i, j ) result( k )

  implicit none
  integer, intent(in) :: i,j
  integer, intent(in) :: a(i:j)
  integer :: k

  k = i + 1

  do while( k<=j .and. a(i) == a(k) ) 
    k = k + 1
  end do

  if(k>j) k = -1

  if(a(i)>a(k)) k = i

end function pivot

end subroutine quick_sort