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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Data.List

main = do
  li <- getLine
  let [n,m] = map read $ words li
  li <- getLine
  let as = map read $ words li
  let ans = compute n m as
  print ans

compute :: Int -> Int -> [Int] -> Int
compute n m as = sum (ass !! m)
  where
    as0 = sortBy c as
    ass = iterate f as0

c = flip compare
f (a:as) = insertBy c (div a 2) as

{-
最大のものを取り出し、半分にし、戻す。
という作業をM回繰り返し、残った値の和が答え。

最大のものが簡単に取り出せるヒープのようなデータ構造を使うべき問題だ。
sortBy, insertBy で間に合うだろうか？
-}