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D - ±1 Operation 2

Score : $400$ points

Problem Statement

You are given a sequence of length $N$: $A=(A_1,A_2,\dots,A_N)$. The following action on this sequence is called an operation.

• First, choose an integer $i$ such that $1 \le i \le N$.
• Next, choose and do one of the following.
  • Add $1$ to $A_i$.
  • Subtract $1$ from $A_i$.

Answer $Q$ questions.
The $i$-th question is the following.

• Consider performing zero or more operations to change every element of $A$ to $X_i$. Find the minimum number of operations required to do so.

Constraints

• All values in input are integers.
• $1 \le N,Q \le 2 \times 10^5$
• $0 \le A_i \le 10^9$
• $0 \le X_i \le 10^9$

Input

Input is given from Standard Input in the following format:

$N$ $Q$

$A_1$ $A_2$ $\dots$ $A_N$

$X_1$

$X_2$

$\vdots$

$X_Q$

Output

Print $Q$ lines.
The $i$-th line should contain the answer to the $i$-th question as an integer.

5 3
6 11 2 5 5
5
20
0

10
71
29

We have $A=(6,11,2,5,5)$ and three questions in this input.

For the $1$-st question, you can change every element of $A$ to $5$ in $10$ operations as follows.

• Subtract $1$ from $A_1$.
• Subtract $1$ from $A_2$ six times.
• Add $1$ to $A_3$ three times.

It is impossible to change every element of $A$ to $5$ in $9$ or fewer operations.

For the $2$-nd question, you can change every element of $A$ to $20$ in $71$ operations.

For the $3$-rd question, you can change every element of $A$ to $0$ in $29$ operations.

10 5
1000000000 314159265 271828182 141421356 161803398 0 777777777 255255255 536870912 998244353
555555555
321654987
1000000000
789456123
0

3316905982
2811735560
5542639502
4275864946
4457360498

The output may not fit into $32$-bit integers.