Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

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

Sample Output 1

60
1
120

In the first query, 30 out of the initial 90 grams of sand will drop from bulb A, resulting in 60 grams.
In the second query, the initial 1 gram of sand will drop from bulb A, and nothing will happen for the next 59 seconds. Then, we will turn over the sandglass, and 1 second after this, bulb A contains 1 gram of sand at the time in question.

Sample Input 2

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

Sample Output 2

100
10
0
0

In every query, the upper bulb initially contains 100 grams, and the question in time comes before we turn over the sandglass.

Sample Input 3

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

Sample Output 3

19
52
91
10
58
42
100

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;
import java.util.List;
import java.util.function.*;

class Main {
    static Scanner scanner = new Scanner();
    static int mod = 1000000007;
    static int inf = 0x7ffffff;

    static long max;
    static long min;
    static long value;
    static long x;
    void solve() {
        x = scanner.nextInt();
        int k = scanner.nextInt();
        List<long[]> queryList = new ArrayList<>();
        long sum = 0;
        for (int i = 0; i < k; i++) {
            long r = scanner.nextInt();
            sum += i % 2 == 0 ? r : -r;
            queryList.add(new long[] {1, r, sum});
        }
        int q = scanner.nextInt();
        for (int i = 0; i < q; i++) {
            queryList.add(new long[] {0, scanner.nextInt(), scanner.nextInt()});
        }
        queryList.sort(Comparator.<long[]>comparingLong(p -> p[1]).thenComparingLong(p -> p[0]));
        boolean b = true;
        min = 0;
        max = x;
        value = 0;
        long last = 0;
        for (long[] query : queryList) {
            update(b ? last - query[1] : query[1] - last);
            if (query[0] == 0) {
                System.out.println(get(query[2]));
            } else if (query[0] == 1) {
                b = !b;
            }
            last = query[1];
        }
    }

    static long get(long a) {
        if (min == max) {
            return value;
        } else if (a <= min) {
            return value;
        } else if (a <= max) {
            return value + a - min;
        } else {
            return value + max - min;
        }
    }

    static void update(long add) {
        if (add < 0) {
            if (get(x) + add < 0) {
                value = 0;
                min = max;
            } else if (value + add < 0) {
                min -= value + add;
                value = 0;
            } else {
                value += add;
            }
        } else if (0 < add) {
            if (x <= value + add) {
                value = x;
                max = min;
            } else if (x <= get(x) + add) {
                max -= get(x) + add - x;
                value += add;
            } else {
                value += add;
            }
        }
    }

    public static void main(String[]$) {
        try {
            new Main().solve();
            System.out.flush();
        } catch (Throwable t) {
            System.out.flush();
            t.printStackTrace();
        }
    }
}

class System {
    static PrintWriter out = new PrintWriter(java.lang.System.out);

    static void exit() {
        java.lang.System.exit(0);
    }
}

class Scanner {
    private BufferedReader reader = new BufferedReader(new InputStreamReader(java.lang.System.in), 0x10000);
    private StringTokenizer tokenizer;

    String next() {
        try {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
        } catch (IOException ignored) {
        }
        return tokenizer.nextToken();
    }

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

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

    char[][] nextCharArray(int n, int m) {
        char[][] a = new char[n][m];
        for (int i = 0; i < n; i++) {
            a[i] = next().toCharArray();
        }
        return a;
    }

    int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    int[] nextIntArray(int n, IntUnaryOperator op) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsInt(nextInt());
        }
        return a;
    }

    long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextLong();
        }
        return a;
    }

    long[] nextLongArray(int n, LongUnaryOperator op) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsLong(nextLong());
        }
        return a;
    }
}