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.

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