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 $A_1, A_2, \dots, A_N$.

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.

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.