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