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 (1.15.1) (judge verdict: Accepted)

use std::cmp;
use std::collections::VecDeque;

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 k: usize = sc.read();
    let turns: Vec<i64> = sc.vec(k);

    let q: usize = sc.read();
    let queries = (0..q)
        .map(|_| (sc.read::<i64>(), sc.read::<i64>()))
        .collect::<Vec<_>>();

    let mut events = vec![];
    for turn in turns.into_iter() {
        events.push((turn, true, 0));
    }

    for i in 0..q {
        let (t, _) = queries[i];
        events.push((t, false, i));
    }
    events.sort();

    let mut sands = vec![];
    for i in 0..q {
        let (_, a) = queries[i];
        sands.push((a, i));
    }
    sands.sort();
    let mut sands = VecDeque::from(sands);

    let mut prev = 0;
    let mut decreasing = true;
    let mut effect = 0;
    let mut is_left = vec![false; q];
    let mut is_right = vec![false; q];
    let mut left = 0;
    let mut right = x;
    for (time, is_turn, query_id) in events.into_iter() {
        if is_turn {
            let d_time = time - prev;

            if decreasing {
                effect -= d_time;
                while let Some((sand, query_id)) = sands.pop_front() {
                    if sand + effect > 0 {
                        sands.push_front((sand, query_id));
                        break;
                    } else {
                        is_left[query_id] = true;
                    }
                }
                left = cmp::max(left - d_time, 0);
                right = cmp::max(right - d_time, 0);
            } else {
                effect += d_time;
                while let Some((sand, query_id)) = sands.pop_back() {
                    if sand + effect < x {
                        sands.push_back((sand, query_id));
                        break;
                    } else {
                        is_right[query_id] = true;
                    }
                }
                left = cmp::min(left + d_time, x);
                right = cmp::min(right + d_time, x);
            }

            prev = time;
            decreasing = !decreasing;
        } else {
            let d_time = time - prev;
            let (left, right, effect) = if decreasing {
                (
                    cmp::max(left - d_time, 0),
                    cmp::max(right - d_time, 0),
                    effect - d_time,
                )
            } else {
                (
                    cmp::min(left + d_time, x),
                    cmp::min(right + d_time, x),
                    effect + d_time,
                )
            };

            if is_right[query_id] {
                println!("{}", right);
            } else if is_left[query_id] {
                println!("{}", left);
            } else {
                let (_, a) = queries[query_id];
                let ans = cmp::max(0, cmp::min(x, a + effect));
                println!("{}", ans);
            }
        }
    }
}

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 {
        IO(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()
    }
}