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: Accepted)

-- https://github.com/minoki/my-atcoder-solutions
import Data.Char (isSpace)
import Data.Int (Int64)
import Data.List (unfoldr)
import qualified Data.ByteString.Char8 as BS
import qualified Data.IntMap.Strict as IntMap
import Data.Monoid

discount :: Int -> IntMap.IntMap Int -> IntMap.IntMap Int
discount 0 p = p
discount m p = case IntMap.maxViewWithKey p of
                  Nothing -> p
                  Just ((k, l), p')
                    | m < l -> IntMap.insertWith (+) (k `quot` 2) m $ IntMap.insert k (l - m) p'
                    | otherwise -> discount (m - l) $ IntMap.insertWith (+) (k `quot` 2) l p'

main = do
  [n,m] <- unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  p <- IntMap.fromListWith (+) . map (\x -> (x,1)) . unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  let result :: Int64
      result = getSum $ IntMap.foldMapWithKey (\k l -> Sum $! fromIntegral k * fromIntegral l) $ discount m p
  print result