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.io.*;
import java.util.*;

public class Main {

	void submit() {
		int x = nextInt();
		int k = nextInt();
		int[] flip = new int[k];
		for (int i = 0; i < k; i++) {
			flip[i] = nextInt();
		}
		
		int q = nextInt();
		
		Function func = new Function(x);
		
		int dir = -1;
		
		int ptr = 0;
		
		int curT = 0;
		
		while (q-- > 0) {
			int t = nextInt();
			int qx = nextInt();
			
			while (ptr < k && flip[ptr] <= t) {
				func.modify(flip[ptr] - curT, dir);
				curT = flip[ptr];
				dir *= -1;
				ptr++;
			}
			
			func.modify(t - curT, dir);
			curT = t;
			
			out.println(func.getAt(qx));
		}
	}
	
	static class Function {
		int flipX;
		int flipY;
		int len;
		
		final int X;

		public Function(int x) {
			flipX = 0;
			flipY = 0;
			len = x;
			this.X = x;
		}
		
		int getAt(int x) {
			if (x <= flipX) {
				return flipY;
			}
			if (x >= flipX + len) {
				return flipY + len;
			}
			return flipY + x - flipX;
		}
		
		void modify(int dist, int dir) {
			flipY += dist * dir;
			if (flipY + len <= 0) {
				flipX = flipY = len = 0;
				return;
			}
			if (flipY >= X) {
				flipX = len = 0;
				flipY = X;
				return;
			}
			
			if (flipY < 0) {
				int delta = -flipY;
				flipX += delta;
				len -= delta;
				flipY = 0;
				return;
			}
			if (flipY + len > X) {
				int delta = flipY + len - X;
				len -= delta;
				return;
			}
		}
	}

	void preCalc() {

	}

	void stress() {

	}

	void test() {

	}

	Main() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		preCalc();
		submit();
		//stress();
		//test();
		out.close();
	}

	static final Random rng = new Random();

	static int rand(int l, int r) {
		return l + rng.nextInt(r - l + 1);
	}

	public static void main(String[] args) throws IOException {
		new Main();
	}

	BufferedReader br;
	PrintWriter out;
	StringTokenizer st;

	String nextToken() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return st.nextToken();
	}

	String nextString() {
		try {
			return br.readLine();
		} catch (IOException e) {
			throw new RuntimeException(e);
		}
	}

	int nextInt() {
		return Integer.parseInt(nextToken());
	}

	long nextLong() {
		return Long.parseLong(nextToken());
	}

	double nextDouble() {
		return Double.parseDouble(nextToken());
	}
}
