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 Ruby (2.3.3) (judge verdict: Accepted)

DBG = !true
n,q = gets.split.map{|x| x.to_i}
a = gets.split.map{|x| x.to_i}
xx = []
for i in 0...q
  xx << gets.to_i
end
if DBG
  print "n #{n} q #{q} x: "
  print xx
  puts ""
  print "a: "
  print a
  puts ""
end

sum = 0
acc = []
eoacc = Array.new(n+2)
for i in 0...n
  sum += a[i]
  acc << sum
end
esum = 0
osum = 0
for i in 0..(n/2)
  break if 2*i == n
  esum += a[2*i]
  eoacc[2*i] = esum
  break if 2*i+1 == n
  osum += a[2*i+1]
  eoacc[2*i+1] = osum
end

for x in xx
  # decide T by binary search
  puts "x #{x} start" if DBG
  if n <= 2
    puts "#{a[n-1]}"
    next
  elsif n <= 4
    if DBG
      puts "x #{x} an2 #{a[n-2]} an3 #{a[n-3]} mid #{(a[n-2]+a[n-3])/2}"
    end
    puts "#{a[n-1] + (x>(a[n-2]+a[n-3])/2 ? a[n-3] : a[n-2])}"
    next
  elsif 2*x > (a[n-2]+a[n-3])
    puts "#{eoacc[n-1]}"
    next
  end
  bot = 1
  ceil = (n-1)/2
  while ceil - bot > 1
    t = (bot + ceil)/2
    y = a[n-t] + a[n-2*t+1]
    z = a[n-t-1] + a[n-2*t-1]
    if y >= 2*x
      bot = t
    elsif 2*x > z
      ceil = t
    end
    if DBG
      puts "t #{t} y #{y} z #{z} bot #{bot} ceil #{ceil} 2x #{2*x}"
      puts "   ant #{a[n-t]} an2tp1 #{a[n-2*t+1]}"
      puts "   ant1 #{a[n-t-1]} an2tm1 #{a[n-2*t-1]}"
    end
  end
  ans = -1
  puts "now bot #{bot}" if DBG
  for t in [bot-3, 1].max..[bot+3,(n+1)/2-1].min
    puts "t=#{t}" if DBG
    y = a[n-t] + a[n-2*t+1]
    z = a[n-t-1] + a[n-2*t-1]
    if y >= 2*x && 2*x > z
      ans = t
      break
    end
  end
  puts "ANSWER: #{ans}" if DBG

  if ans == -1
    val = acc[n-1] - acc[n/2 - 1]
  else
    puts "n/2 #{n/2} ans #{ans} eacc #{eacc[n/2-ans]}" if DBG
    val = acc[n-1] - acc[n-ans-1] + eoacc[n - 2*ans - 1]
  end
  puts "#{val}"
end