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 Rust (1.42.0) (judge verdict: Accepted)

use std::cmp;

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());

    let x: i64 = sc.read();
    let mut events = vec![];
    let k: usize = sc.read();
    for _ in 0..k {
        let r: i64 = sc.read();
        events.push((r, true, (0, 0)));
    }

    let q: usize = sc.read();
    let mut ans = vec![0; q];
    for i in 0..q {
        let t: i64 = sc.read();
        let a: i64 = sc.read();
        events.push((t, false, (a, i)));
    }

    events.sort();

    let mut min = 0;
    let mut max = x;
    let mut lower = 0;
    let mut upper = x;
    let mut up = true;
    let mut prev_turn = 0;
    for (time, is_turn, (a, i)) in events.into_iter() {
        let dt = time - prev_turn;
        if is_turn {
            if up {
                if min < dt {
                    let d = dt - min;
                    lower += d;
                }

                max = cmp::max(max - dt, 0);
                min = cmp::max(min - dt, 0);
            } else {
                if max + dt > x {
                    let d = max + dt - x;
                    upper -= d;
                }

                max = cmp::min(max + dt, x);
                min = cmp::min(min + dt, x);
            }

            up = !up;
            prev_turn = time;
        } else {
            let mut lower = lower;
            let mut upper = upper;
            let mut min = min;
            let mut max = max;
            if up {
                if min < dt {
                    let d = dt - min;
                    lower += d;
                }

                max = cmp::max(max - dt, 0);
                min = cmp::max(min - dt, 0);
            } else {
                if max + dt > x {
                    let d = max + dt - x;
                    upper -= d;
                }

                max = cmp::min(max + dt, x);
                min = cmp::min(min + dt, x);
            }

            if lower <= a && a <= upper {
                assert_eq!(upper - lower, max - min);
                assert_eq!(max - (upper - a), min + (a - lower));
                ans[i] = min + (a - lower);
            } else if a < lower {
                ans[i] = min;
            } else {
                ans[i] = max;
            }
        }

        if upper >= lower {
            assert_eq!(upper - lower, max - min);
        } else {
            assert_eq!(max, min);
        }
    }

    for ans in ans.into_iter() {
        sc.write(ans);
        sc.write("\n");
    }
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> Self {
        Self(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}