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.

Examples

Input

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


Output

60
1
120


Input

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


Output

100
10
0
0


Input

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


Output

19
52
91
10
58
42
100
import java.util.Scanner;

public class Main {

	private void solve() {
		Scanner in = new Scanner(System.in);
		int X = in.nextInt();
		int K = in.nextInt();
		int[] r = new int[K];
		for (int i = 0; i < K; i++) {
			r[i] = in.nextInt();
		}
		int Q = in.nextInt();
		int[] t = new int[Q];
		int[] a = new int[Q];
		for (int i = 0; i < Q; i++) {
			t[i] = in.nextInt();
			a[i] = in.nextInt();
		}
		int rp = 0;
		int tap = 0;
		
		int low = 0;
		int middle = 0;
		int high = X;
		int l_bound = 0;
		int h_bound = X;
		
		int prev_r = 0;
		while(tap<Q){
			if(rp>=K || t[tap]<=r[rp]){
				if(rp%2==0){ // now down
					if(a[tap]<=l_bound){
						System.out.println(Math.max(0,low-(t[tap]-prev_r)));
					}else if(a[tap]>=h_bound){
						System.out.println(Math.max(0, high-(t[tap]-prev_r)));
					}else{
						System.out.println(Math.max(0, a[tap]+middle-(t[tap]-prev_r)));
					}
				}else{// now up
					if(a[tap]<=l_bound){
						System.out.println(Math.min(X,low+(t[tap]-prev_r)));
					}else if(a[tap]>=h_bound){
						System.out.println(Math.min(X, high+(t[tap]-prev_r)));
					}else{
						System.out.println(Math.min(X, a[tap]+middle+(t[tap]-prev_r)));
					}
				}
				tap ++;
			}else{
				if(rp%2==0){//down
					middle -= r[rp]-prev_r;
					low = Math.max(0, low-(r[rp]-prev_r));
					high = Math.max(0, high-(r[rp]-prev_r));
				}else{// up
					middle += r[rp]-prev_r;
					low = Math.min(X, low+(r[rp]-prev_r));
					high = Math.min(X, high+(r[rp]-prev_r));
				}
				if(l_bound+middle<0){
					l_bound = -middle;
				}
				if(h_bound+middle>X){
					h_bound = X -middle;
				}
				prev_r = r[rp];
				rp ++;
			}
		}
	}
	
	public static void main(String[] args) {
		new Main().solve();
	}
}