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 OCaml (4.02.3) (judge verdict: Accepted)

module M = Map.Make (struct
  type t = int
  let compare = compare
end)
let n, m = Scanf.scanf " %d %d" @@ fun a b -> a, b
let a_s = Array.init n @@ fun _ -> Scanf.scanf " %d" (+) 0
let im = ref M.empty
let g a = im := M.add a (1 + try M.find a !im with _ -> 0) !im
let h a = im := match M.find a !im with 1 -> M.remove a !im | c -> M.add a (c - 1) !im
let rec f i = if i >= m then M.fold (fun a c s -> s + a * c) !im 0
  else let a, _ = M.max_binding !im in g @@ a / 2; h a; f @@ i + 1
let _ = Array.iter g a_s; Printf.printf "%d\n" @@ f 0