Problem:
Score : 700 points

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.

Sample Input 1

180
3
60 120 180
3
30 90
61 1
180 180

Sample Output 1

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.

Sample Input 2

100
1
100000
4
0 100
90 100
100 100
101 100

Sample Output 2

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.

Sample Input 3

100
5
48 141 231 314 425
7
0 19
50 98
143 30
231 55
342 0
365 100
600 10

Sample Output 3

19
52
91
10
58
42
100

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		int[] TT = new int[K+1];
		int[] La = new int[K+1];
		int[] Lv = new int[K+1];
		int[] Ra = new int[K+1];
		int[] Rv = new int[K+1];
		
		for(int i=1;i<=K;i++){
			TT[i] = R[i - 1];
		}
		
		La[0] = 0;
		Lv[0] = 0;
		Ra[0] = X;
		Rv[0] = X;
		for(int i=1;i<=K;i++){
			int lose = TT[i] - TT[i-1];
			int l = Lv[i-1] - lose;
			La[i] = La[i-1];
			if(l <= 0) La[i] += (-l);
			Lv[i] = X - Math.Max(0, l);
			
			int r = Rv[i-1] - lose;
			Ra[i] = Ra[i-1];
			if(r <= 0) Ra[i] -= (-r);
			Rv[i] = X - Math.Max(0, r);
			
		}
		
//		Console.WriteLine(String.Join("\t",La));
//		Console.WriteLine(String.Join("\t",Lv));
//		Console.WriteLine(String.Join("\t",Ra));
//		Console.WriteLine(String.Join("\t",Rv));
		
		int[] ans = new int[Q];
		for(int q=0;q<Q;q++){
			int t = T[q];
			int a = A[q];
			
			int l = 0;
			int r = K + 1;
			while(r - l > 1){
				int c = (l + r) / 2;
				if(TT[c] <= t){
					l = c;
				} else {
					r = c;
				}
			}
			
			int iniTime = l;
			int lose = t - TT[iniTime];
			
			int iniValue = 0;
			if(Lv[iniTime] == Rv[iniTime]){
				iniValue = Lv[iniTime];
			} else {
				if(a <= La[iniTime]){
					iniValue = Lv[iniTime];
				} else if(a >= Ra[iniTime]){
					iniValue = Rv[iniTime];
				} else {
					if(Lv[iniTime] < Rv[iniTime]){
						iniValue = Lv[iniTime] + (a - La[iniTime]);
					} else {
						iniValue = Lv[iniTime] - (a - La[iniTime]);
					}
				}
			}
			
			ans[q] = iniTime % 2 == 0 ? Math.Max(0, iniValue - lose) : Math.Max(0, X -Math.Max(0, iniValue - lose));
		}
		
		
		Console.WriteLine(String.Join("\n",ans));
	}
	int X;
	int K;
	int[] R;
	int Q;
	int[] T;
	int[] A;
	
	
	public Sol(){
		X = ri();
		K = ri();
		R = ria();
		Q = ri();
		T = new int[Q];
		A = new int[Q];
		for(int i=0;i<Q;i++){
			var d = ria();
			T[i] = d[0]; A[i] = d[1];
		}
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}