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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

typedef struct {
  int A;
  int B;
  int up;
} SAND;

SAND s;

void initsand(int X, int a) {
  s.A = a;
  s.B = (X - a);
  s.up = 'A';
}

void dropsand(int *r, int t, int K) {
  int T = 0, L = 0, i;
  for (i = 0; i < K && t > 0; i++) {
    T = *(r + i) - L;
    L = *(r + i);
    while (T > 0 && t > 0) {
      if (s.up == 'A') {
        if (s.A >0) {
          s.A--;
          s.B++;
        }
      } else {
        if (s.B > 0) {
          s.B--;
          s.A++;
        }
      }
      T--;
      t--;
    }
    if (s.up == 'A') s.up = 'B';
    else s.up = 'A';
  }
}

int main() {
  int X, K, *r, Q, i, *q, a, t;

  scanf("%d", &X);
  scanf("%d", &K);
  r = (int*)malloc(sizeof(int) * K);
  for (i = 0; i < K; i++) {
    scanf("%d", (r + i));
  }
  scanf("%d", &Q);
  q = (int*)malloc(sizeof(int) * Q);
  for (i = 0; i < Q; i++) {
    scanf("%d %d", &t, &a);
    initsand(X, a);
    dropsand(r, t, K);
    *(q + i) = s.A;
  }

  for (i = 0; i < Q; i++) {
    printf("%d\n", *(q + i));
  }
  return 0;
}