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.

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.

Constraints

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

Sample Input 1

5 3
6 11 2 5 5
5
20
0

Sample Output 1

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.

Sample Input 2

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

Sample Output 2

3316905982
2811735560
5542639502
4275864946
4457360498

The output may not fit into 32-bit integers.

见题面 Input 部分

见题面 Output 部分