Problem Statement

We have a sandglass consisting of two bulbs, bulb A and bulb B. These bulbs contain some amount of sand. When we put the sandglass, either bulb $A$ or $B$ lies on top of the other and becomes the upper bulb. The other bulb becomes the lower bulb.

The sand drops from the upper bulb to the lower bulb at a rate of $1$ gram per second. When the upper bulb no longer contains any sand, nothing happens.

Initially at time $0$, bulb A is the upper bulb and contains $a$ grams of sand; bulb B contains $X-a$ grams of sand (for a total of $X$ grams).

We will turn over the sandglass at time $r_1,r_2,..,r_K$. Assume that this is an instantaneous action and takes no time. Here, time $t$ refer to the time $t$ seconds after time $0$.

You are given $Q$ queries. Each query is in the form of $(t_i,a_i)$. For each query, assume that $a=a_i$ and find the amount of sand that would be contained in bulb A at time $t_i$.

Constraints

• $1≤X≤10^9$
• $1≤K≤10^5$
• $1≤r_1<r_2< .. <r_K≤10^9$
• $1≤Q≤10^5$
• $0≤t_1<t_2< .. <t_Q≤10^9$
• $0≤a_i≤X (1≤i≤Q)$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

X
K
r_1 r_2 .. r_K
Q
t_1 a_1
t_2 a_2
:
t_Q a_Q

Output

For each query, print the answer in its own line.