Problem:
Score : 500 points

Problem Statement

There are N cards. The i-th card has an integer A_i written on it.
For any two cards, the integers on those cards are different.

Using these cards, Takahashi and Aoki will play the following game:

Aoki chooses an integer x.

Starting from Takahashi, the two players alternately take a card. The card should be chosen in the following manner:

Takahashi should take the card with the largest integer among the remaining card.

Aoki should take the card with the integer closest to x among the remaining card. If there are multiple such cards, he should take the card with the smallest integer among those cards.

The game ends when there is no card remaining.

You are given Q candidates for the value of x: X_1, X_2, ..., X_Q.
For each i (1 \leq i \leq Q), find the sum of the integers written on the cards that Takahashi will take if Aoki chooses x = X_i.

Constraints

2 \leq N \leq 100 000

1 \leq Q \leq 100 000

1 \leq A_1 < A_2 < ... < A_N \leq 10^9

1 \leq X_i \leq 10^9 (1 \leq i \leq Q)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N Q
A_1 A_2 ... A_N
X_1
X_2
:
X_Q

Output

Print Q lines. The i-th line (1 \leq i \leq Q) should contain the answer for x = X_i.

Sample Input 1

5 5
3 5 7 11 13
1
4
9
10
13

Sample Output 1

31
31
27
23
23

For example, when x = X_3(= 9), the game proceeds as follows:

Takahashi takes the card with 13.

Aoki takes the card with 7.

Takahashi takes the card with 11.

Aoki takes the card with 5.

Takahashi takes the card with 3.

Thus, 13 + 11 + 3 = 27 should be printed on the third line.

Sample Input 2

4 3
10 20 30 40
2
34
34

Sample Output 2

70
60
60

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE TupleSections #-}
{-# LANGUAGE ExplicitForAll #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE MultiWayIf #-}
{-# LANGUAGE Unsafe #-}
{-# LANGUAGE RecordWildCards #-}
{-# LANGUAGE FlexibleContexts #-}

import Data.Bits
import Data.List
import qualified Data.ByteString.Char8 as BS
import qualified Data.ByteString.Lazy.Char8 as BSL
import Data.IntMap.Strict (IntMap)
import qualified Data.IntMap.Strict as IMS
import Data.IntSet (IntSet)
import qualified Data.IntSet as IS
import qualified Data.Sequence as Seq
import Data.Sequence (Seq)
import qualified Data.Array.IArray as A
import qualified Data.Array.MArray.Safe as A
import qualified Data.Array.MArray as A
import Data.Array (Array)
import Data.Array.Unboxed (UArray)
import Data.Array.IArray (IArray)
import Data.Array.MArray.Safe (MArray)
import Data.Array.IO.Safe (IOArray, IOUArray)
import Data.Array.ST.Safe (STArray, STUArray, runSTArray, runSTUArray)
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import Control.Monad
import Control.Monad.ST
-- import Control.Monad.ST.Safe
import Control.Applicative
import Data.Maybe
import Data.Tuple
import Data.Ord
import Control.Monad.State.Strict
import Data.Int
import System.IO
import Data.Function
import Control.Monad.Primitive
import qualified Data.Vector.Primitive.Mutable as VPM
import qualified Data.Vector.Generic.Mutable as VGM
import Data.STRef
import Data.IORef

main :: IO ()
main = do
  [n,q] <- map read . words <$> getLine :: IO [Int]
  as <- VU.unfoldrN n (BS.readInt . BS.dropWhile (==' ')) <$> BS.getLine
  let asum = VU.scanl' (+) 0 as
      aIntSum = VU.map fst $ VU.scanl' (\(!x,!y) a -> (y+a,x)) (0,0) as
  xs <- VU.unfoldrN q (BSL.readInt . BSL.dropWhile (<'!')) <$> BSL.getContents
  VU.forM_ xs $ \x ->
    print (query n as asum aIntSum x :: Int)

query n as asum aIntSum x
  = asum VU.! n - asum VU.! (n-divpt) + aIntSum VU.! (max 0 $ n-divpt*2)
  where
    -- How many entries >= x can takahashi take?
    divpt = (gone+1) `shiftR` 1
    -- How many cards are taken before all cards >= x are gone?
    gone = gone_binSearch 0 $ n+1
    gone_binSearch :: Int -> Int -> Int
    gone_binSearch !ok !ng -- at least ok cards are taken; ng cards are never.
      | ng - ok <= 1 = ok
      | as VU.! (n - (mid+1) `shiftR` 1) - x >= x - as VU.! (n - mid)
        = gone_binSearch mid ng
      | otherwise = gone_binSearch ok mid
      where
        mid = (ok + ng) `shiftR` 1