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::io::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[derive(Clone, Debug)]
struct State {
    t: i64,
    lower: i64,
    upper: i64,
    lower_value: i64,
    upper_value: i64,
    dir: i64,
}

impl State {
    fn new(t: i64, lower: i64, upper: i64, lower_value: i64, upper_value: i64, dir: i64) -> State {
        State {
            t: t,
            lower: lower,
            upper: upper,
            lower_value: lower_value,
            upper_value: upper_value,
            dir: dir,
        }
    }
}

fn main() {
    let x = read::<i64>();
    let k = read::<usize>();
    let mut rseq = vec![0; k];
    for i in 0..k {
        rseq[i] = read::<i64>();
    }
    let q = read::<usize>();
    let mut query = vec![(0, 0); q];
    for i in 0..q {
        query[i] = (read::<i64>(), read::<i64>());
    }
    let mut state = State::new(0, 0, x, 0, 0, -1);
    let mut states = vec![];
    states.push(state.clone());
    for i in 0..k {
        let d = rseq[i] - state.t;
        let nt = rseq[i];
        let mut nlower = std::cmp::min(x, state.lower + d * state.dir);
        let mut nupper = std::cmp::max(0, state.upper + d * state.dir);
        let mut nlower_value = state.lower_value;
        let mut nupper_value = state.upper_value;
        let ndir = state.dir * -1;
        if nlower < 0 {
            nlower_value = std::cmp::min(x - nupper_value, nlower_value - nlower);
            nlower = 0;
        }
        if nupper > x {
            nupper_value = std::cmp::min(x - nlower_value, nupper_value - (x - nupper));
            nupper = x;
        }
        state = State::new(nt, nlower, nupper, nlower_value, nupper_value, ndir);
        // println!("{:?}", state);
        assert!(nupper >= nlower);
        assert!(nupper - nlower + nlower_value + nupper_value == x);
        states.push(state.clone());
    }
    for i in 0..q {
        let index = match states.binary_search_by(|state| state.t.cmp(&query[i].0)) {
            Ok(v) => v,
            Err(v) => v - 1,
        };
        let state = &states[index];
        let d = query[i].0 - state.t;
        let mut pos = query[i].1 - state.lower_value + state.lower;
        pos = std::cmp::max(pos, state.lower);
        pos = std::cmp::min(pos, state.upper);
        pos += d * state.dir;
        pos = std::cmp::max(pos, 0);
        pos = std::cmp::min(pos, x);
        println!("{}", pos);
    }
}