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.Arrays;

public class Main {

  private static void solve() {
    long x = nl();
    int k = ni();
    long[] r = nal(k);
    int qq = ni();
    long[][] query = new long[qq + k][2];
    for (int i = 0; i < qq; i ++) {
      query[i][0] = nl();
      query[i][1] = nl();
    }
    for (int i = 0; i < k; i ++) {
      query[i + qq][0] = r[i];
      query[i + qq][1] = -1;
    }
    Arrays.sort(query, (o1, o2) -> Long.compare(o1[0], o2[0]));
    
    //f_t(x) =
    //  a + c (0 <= x <= a)
    //  x + c (a <= x <= b)
    //  b + c (b <= x < X)

    long a = 0;
    long b = x;
    long c = 0;
    long t = 0;
    boolean up = true;
    
    for (long[] q : query) {
      long[] next = f(q[0] - t, a, b, c, x, up);
      if (q[1] < 0) {
        up = !up;
      } else {
        if (q[1] < next[0]) {
          out.println(next[0] + next[2]);
        } else if (q[1] > next[1]) {
          out.println(next[1] + next[2]);
        } else {
          out.println(q[1] + next[2]);
        }
        out.flush();
      }
      t = q[0];
      a = next[0];
      b = next[1];
      c = next[2];
    }
  }
  
  private static long[] f(long d, long a, long b, long c, long X, boolean up) {
    long[] ret = new long[3];
    if (up) {
      ret[0] = a + c > d ? a : Math.min(d - c, X);
      ret[1] = Math.max(b, ret[0]);
      ret[2] = Math.max(c - d, -X);
    } else {
      ret[1] = b + c + d < X ? b : Math.max(X - (c + d), 0);
      ret[0] = Math.min(ret[1], a);
      ret[2] = Math.min(c + d, X);
    }
    return ret;
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = System.getProperty("debug");
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}
