
Score : 700 points
Problem StatementWe 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.
InputThe 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
OutputFor each query, print the answer in its own line.
Sample Input 1180
3
60 120 180
3
30 90
61 1
180 180
Sample Output 160
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.
Sample Input 2100
1
100000
4
0 100
90 100
100 100
101 100
Sample Output 2100
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.
Sample Input 3100
5
48 141 231 314 425
7
0 19
50 98
143 30
231 55
342 0
365 100
600 10
Sample Output 319
52
91
10
58
42
100
