Problem Statement

You are given a list of ~n~ integers ~X = [x_1,\ x_2,\ ...,\ x_n]~. Now, imagine you have a list ~P~ of all pairings of integers from ~1~ to ~n~ such that ~P~ is sorted in increasing order. In other words, you have:

\begin{array}{rcc} P &=& \Big[\ \normalsize(1, 1), (1, 2), (1, 3), ..., (1, n),\ & & \ \ \ (2, 1), (2, 2), (2, 3), ..., (2, n), \ & & \ ...\ & & \ \ \ \ \ \ (n, 1), (n, 2), (n, 3), ..., (n, n)\ \Big]\normalsize \ \end{array}

Now, you are given ~Q~ queries, each will contain a single integer ~q_i~ such that ~1 \leq q_i \leq |P|~, given some ~q_i~ you should determine ~f(q_i)~:

\begin{array}{rcl} f(k) &=& \sum_{i=1}^{k} x_{P_i[0]} - x_{P_i[1]} \end{array}

In other words, ~f(k)~ takes the first ~k~ pairs in ~P~, and for each pair ~(a, b)~ it will calculate ~x_a - x_b~ and sum all of them together.

Input Format

Your first line will contain two space-separated integers ~n~ and ~q~

Your next line will contain ~n~ space-separated integers ~x_1~ through ~x_n~.

Your next ~Q~ lines will contain one integer each, the ~i^{th}~ of which representing ~q_i~.

Output Format

You should output a single integer for each query (in the same order the queries appear), the ~i^{th}~ of which should be ~f(q_i)~.

Constraints

• ~1 \leq n, q \leq 10^5~
• ~1 \leq q_i \leq n^2~
• ~-10^3 \leq x_i \leq 10^3~

Sample Cases

Input 1

3 3
11 7 5
4
6
9

Output 1

6
8
0

Explanation 1

Here ~P = [(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)]~.

For the first query ~q_1 = 4~, we calculate ~(x_1 - x_1) + (x_1 - x_2) + (x_1 - x_3) + (x_2 - x_1) = (11 - 11) + (11 - 7) + (11 - 5) + (7 - 11) = 6~. For the second query ~q_1 = 6~, we calculate ~(x_1 - x_1) + (x_1 - x_2) + (x_1 - x_3) + (x_2 - x_1) + (x_2 - x_2) + (x_2 - x_3)~. For the third query ~q_1 = 9~, we calculate ~(x_1 - x_1) + (x_1 - x_2) + (x_1 - x_3) + (x_2 - x_1) + (x_2 - x_2) + (x_2 - x_3) + (x_3 - x_1) + (x_3 - x_2) + (x_3 - x_3)~.

Input 2

10 5
-5 10 -1 9 -4 6 3 -1 -7 -5
20
36
8
79
38

Output 2

40
64
-57
126
80

Template

n, q = map(int, input().split())
numbers = list(map(int, input().split()))
queries = [int(input()) for _ in range(q)]

# print your output