Problem Statement

You are given a sequence of N positive integers: $A = (A_1, A_2, \dots, A_N)$, and Q queries.
In the $i-th query (1 \leq i \leq Q)$, given a positive integer K_i, find the K_i-th smallest integer among the positive integers that differ from all of $A_1, A_2, \dots, A_N$.

Input

Input is given from Standard Input in the following format:
N Q
$A_1 A_2 \ldots A_N$
K_1
K_2
$\vdots$
K_Q

Output

Print Q lines. The i-th line should contain the response to the i-th query.

Constraints

• $1 \leq N, Q \leq 10^5$
• $1 \leq A_1 < A_2 < \dots < A_N \leq 10^{18}$
• $1 \leq K_i \leq 10^{18}$
• All values in input are integers.

Sample Input 1

4 3
3 5 6 7
2
5
3

Sample Output 1

2
9
4

The positive integers that differ from all of $A_1, A_2, \dots, A_N$ are $1, 2, 4, 8, 9, 10, 11, \dots$ in ascending order.
The second, fifth, and third smallest of them are 2, 9, and 4, respectively.

Sample Input 2

5 2
1 2 3 4 5
1
10

Sample Output 2

6
15

见题面 Input 部分

见题面 Output 部分