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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.NoSuchElementException;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
import static java.lang.Math.max;
import static java.lang.Math.min;



public class Main {
    public static void main(String[] args) {
        StringBuilder out = new StringBuilder();
        solve(out);
        PrintWriter pw = new PrintWriter(System.out);
        pw.println(out);
        pw.flush();
        pw.close();
    }

    public static void solve(StringBuilder out) {
        long x = In.nl();
        int k = In.ni();
        long[] r = new long[k + 2];
        r[0] = 0;
        for (int i = 1; i <= k; i++) r[i] = In.nl();
        r[k + 1] = (long) 1e9;
        int q = In.ni();
        long u = 0, d = x;
        long xu = 0, xd = x;
        for (int i = 0, j = 0; i < q; i++) {
            long t = In.nl();
            long a = In.nl();
            int lf = 0, rg = k + 1;
            while (rg - lf > 1) {
                int md = (lf + rg) >> 1;
                if (r[md] <= t) lf = md;
                else rg = md;
            }
            while (j < lf) {
                j++;
                if ((j & 1) == 1) {
                    u = max(u, r[j] - r[j - 1] - xu + u);
                    xu = max(0, xu - (r[j] - r[j - 1]));
                    xd = max(0, xd - (r[j] - r[j - 1]));
                } else {
                    d = min(d, d - (r[j] - r[j - 1]) + (x - xd));
                    xu = min(x, xu + (r[j] - r[j - 1]));
                    xd = min(x, xd + (r[j] - r[j - 1]));
                }
            }
            a = a <= u ? xu : a >= d ? xd : xu + a - u;
            out.append((j & 1) == 0 ? max(0, a - (t - r[j])) : min(x, a + (t - r[j]))).append('\n');
        }
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 */
final class In {
    public static final FastScanner fsc = new FastScanner();
    public static int ni() {return fsc.nextInt();}
    public static int[] ni(final int n) {
        final int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = fsc.nextInt();
        return a;
    }
    public static int[] ni(final int n, final IntUnaryOperator f) {
        final int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = f.applyAsInt(fsc.nextInt());
        return a;
    }
    public static int[][] ni(final int n, final int m) {
        final int[][] a = new int[n][m];
        for (int i = 0; i < n; i++) a[i] = ni(m);
        return a;
    }
    public static int[][] ni(final int n, final int m, final IntUnaryOperator f) {
        final int[][] a = new int[n][m];
        for (int i = 0; i < n; i++) a[i] = ni(m, f);
        return a;
    }
    public static long nl() {return fsc.nextLong();}
    public static long[] nl(final int n) {
        final long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = fsc.nextLong();
        return a;
    }
    public static long[] nl(final int n, final LongUnaryOperator f) {
        final long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = f.applyAsLong(fsc.nextLong());
        return a;
    }
    public static long[][] nl(final int n, final int m) {
        final long[][] a = new long[n][m];
        for (int i = 0; i < n; i++) a[i] = nl(m);
        return a;
    }
    public static long[][] nl(final int n, final int m, final LongUnaryOperator f) {
        final long[][] a = new long[n][m];
        for (int i = 0; i < n; i++) a[i] = nl(m, f);
        return a;
    }
    public static char[] nc() {return fsc.next().toCharArray();}
    public static char[][] nc(final int n) {
        final char[][] c = new char[n][];
        for (int i = 0; i < n; i++) c[i] = nc();
        return c;
    }
    public static double nd() {return fsc.nextDouble();}
    public static double[] nd(final int n) {
        final double[] a = new double[n];
        for (int i = 0; i < n; i++) a[i] = fsc.nextDouble();
        return a;
    }
    public static double[][] nd(final int n, final int m) {
        final double[][] a = new double[n][m];
        for (int i = 0; i < n; i++) a[i] = nd(m);
        return a;
    }
    public static String ns() {return fsc.next();}
    public static String[] ns(final int n) {
        final String[] s = new String[n];
        for (int i = 0; i < n; i++) s[i] = fsc.next();
        return s;
    }
    public static boolean[][] grid(final int h, final int w, final char trueCharacter) {
        final boolean[][] grid = new boolean[h][w];
        for (int i = 0; i < h; i++) {
            final char[] s = fsc.next().toCharArray();
            for (int j = 0; j < w; j++) grid[i][j] = s[j] == trueCharacter;
        }
        return grid;
    }
}


final class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try {buflen = in.read(buffer);}
        catch (final IOException e) {e.printStackTrace();}
        return buflen > 0;
    }
    private int readByte() {return hasNextByte() ? buffer[ptr++] : -1;}
    public boolean hasNext() {
        while (hasNextByte() && !(33 <= buffer[ptr] && buffer[ptr] <= 126)) ptr++;
        return hasNextByte();
    }
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        final StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (33 <= b && b <= 126) {sb.appendCodePoint(b); b = readByte();}
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {minus = true; b = readByte();}
        if (b < '0' || '9' < b) throw new NumberFormatException();
        for (; ; b = readByte()) {
            if ('0' <= b && b <= '9') n = n * 10 + b - '0';
            else if (b == -1 || !(33 <= b && b <= 126)) return minus ? -n : n;
            else throw new NumberFormatException();
        }
    }
    public int nextInt() {return Math.toIntExact(nextLong());}
    public double nextDouble() {return Double.parseDouble(next());}
}
