Score : $700$ points
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 $t_i$.
The input is given from Standard Input in the following format:
$X$ $K$ $r_1$ $r_2$ .. $r_K$ $Q$ $t_1$ $a_1$ $t_2$ $a_2$ $:$ $t_Q$ $a_Q$
For each query, print the answer in its own line.
180 3 60 120 180 3 30 90 61 1 180 180
60 1 120
In the first query, $30$ out of the initial $90$ grams of sand will drop from bulb A, resulting in $60$ grams. In the second query, the initial $1$ gram of sand will drop from bulb A, and nothing will happen for the next $59$ seconds. Then, we will turn over the sandglass, and $1$ second after this, bulb $A$ contains $1$ gram of sand at the time in question.
100 1 100000 4 0 100 90 100 100 100 101 100
100 10 0 0
In every query, the upper bulb initially contains $100$ grams, and the question in time comes before we turn over the sandglass.
100 5 48 141 231 314 425 7 0 19 50 98 143 30 231 55 342 0 365 100 600 10
19 52 91 10 58 42 100