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 {


    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        int X = sc.nextInt();
        int n = sc.nextInt();
        int[] delta = new int[n + 1];
        int f = 0;
        for (int i = 0; i < n; i++) {
            int p = sc.nextInt();
            delta[i] = p - f;
            f = p;
        }
        delta[n] = 1_000_000_000 - f;
        n++;
        int q = sc.nextInt();
        int[][] qs = new int[q][];
        for (int i = 0; i < q; i++) {
            int t = sc.nextInt();
            int a = sc.nextInt();
            qs[i] = new int[]{a, t, i, -1};
        }
        Arrays.sort(qs, new Comparator<int[]>() {
            @Override
            public int compare(int[] t1, int[] t2) {
                return t1[1] - t2[1];
            }
        });
        int curTime = 0;
        int curIdx = 0;
        List<Integer>[] times = new List[n];
        for (int i = 0; i < n; i++) {
            times[i] = new ArrayList<>();
        }
        for (int i = 0; i < n; i++) {
            int nextTime = curTime + delta[i];
            while (curIdx < q && nextTime >= qs[curIdx][1]) {
                qs[curIdx][1] -= curTime;
                times[i].add(qs[curIdx][2]);
                curIdx++;
            }
            curTime = nextTime;
        }
        Arrays.sort(qs, new Comparator<int[]>() {
            @Override
            public int compare(int[] t1, int[] t2) {
                return t1[0] - t2[0];
            }
        });
        int[] mapIdx = new int[q];
        for (int i = 0; i < q; i++) {
            mapIdx[qs[i][2]] = i;
        }
        for (List<Integer> l: times) {
            for (int i = 0; i < l.size(); i++) {
                int t = l.get(i);
                l.set(i, mapIdx[t]);
            }
        }
        boolean useMax = true;
        int front = 0, frontVal = 0;
        int back = q, backVal = X;
        int change = 0;
        for (int i = 0; i < n; i++) {
            for (int idx: times[i]) {
                int curVal;
                if (idx < front) {
                    curVal = frontVal;
                } else if (idx >= back) {
                    curVal = backVal;
                } else {
                    curVal = qs[idx][0] + change;
                }
                if (useMax) {
                    qs[idx][3] = Math.max(0, curVal - qs[idx][1]);
                } else {
                    qs[idx][3] = Math.min(X, curVal + qs[idx][1]);
                }
            }
            if (useMax) {
                frontVal = Math.max(0, frontVal - delta[i]);
                backVal = Math.max(0, backVal - delta[i]);
                int lo = front, hi = back;
                while (lo < hi) {
                    int mid = (lo + hi) >> 1;
                    if (qs[mid][0] + change - delta[i] < 0) {
                        lo = mid + 1;
                    } else {
                        hi = mid;
                    }
                }
                front = lo;
                change -= delta[i];
            } else {
                frontVal = Math.min(X, frontVal + delta[i]);
                backVal = Math.min(X, backVal + delta[i]);
                int lo = front, hi = back;
                while (lo < hi) {
                    int mid = (lo + hi) >> 1;
                    if (qs[mid][0] + change + delta[i] > X) {
                        hi = mid;
                    } else {
                        lo = mid + 1;
                    }
                }
                back = hi;
                change += delta[i];
            }
            useMax = !useMax;
        }
        int[] ret = new int[q];
        for (int i = 0; i < q; i++) {
            ret[qs[i][2]] = qs[i][3];
        }
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < q; i++) {
            sb.append(ret[i]).append('\n');
        }
        System.out.println(sb.toString());
    }

    public static class Scanner {
        StringTokenizer st;
        BufferedReader br;
        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }
        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
            }
            return st.nextToken();
        }
        public int nextInt() throws IOException{
            return Integer.parseInt(next());
        }
    }
}