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;
use std::usize;
use std::cmp;

fn main() {
    let inf = 1000000007;
    let x = read_values::<i64>()[0];
    let k = read_values::<usize>()[0];
    let r = {
        let mut v: Vec<i64> = read_values::<i64>();
        v.push(inf);
        v
    };
    let q = read_values::<usize>()[0];
    let (t, a) = {
        let mut t = vec![inf; q + 1];
        let mut a = vec![inf; q + 1];
        for i in 0..q {
            let v = read_values::<i64>();
            t[i] = v[0];
            a[i] = v[1];
        }
        (t, a)
    };

    let mut y = 0;
    let mut w = 0;
    let mut z = x;
    let mut r_head = 0;
    let mut t_head = 0;
    let mut prev_turn = 0;
    let mut up = true;

    let mut bankrupt = false;
    let mut height = 0;

    while r_head < k || t_head < q {
        if r[r_head] < t[t_head] {
            // turn
            let time = r[r_head] - prev_turn;
            if up {
                y -= time;
                if y < 0 && y.abs() > w {
                    w = y.abs();
                }
            } else {
                y += time;
                if y > 0 && x - y < z {
                    z = x - y;
                }
            }

            if bankrupt && up {
                height = cmp::max(0, height - time);
            } else if bankrupt && !up {
                height = cmp::min(x, height + time);
            } else if !bankrupt && w >= z {
                bankrupt = true;
                if up {
                    height = 0;
                } else {
                    height = x;
                }
            }

            up = !up;
            prev_turn = r[r_head];
            r_head += 1;
        } else {
            // query
            let time = t[t_head] - prev_turn;
            let mut ans = if a[t_head] > z {
                z + y
            } else if a[t_head] < w {
                w + y
            } else {
                a[t_head] + y
            };

            if up {
                ans -= time;
            } else {
                ans += time;
            }

            if bankrupt {
                if up {
                    ans = height - time;
                } else {
                    ans = height + time;
                }
            }

            ans = cmp::min(x, ans);
            ans = cmp::max(0, ans);

            println!("{}", ans);
            t_head += 1;
        }
    }
}

fn read_line() -> String {
    let stdin = io::stdin();
    let mut buf = String::new();
    stdin.read_line(&mut buf).unwrap();
    buf
}

fn read_values<T>() -> Vec<T>
    where T: std::str::FromStr,
          T::Err: std::fmt::Debug
{
    read_line()
        .split(' ')
        .map(|a| a.trim().parse().unwrap())
        .collect()
}