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