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.

Examples

Input

180
3
60 120 180
3
30 90
61 1
180 180


Output

60
1
120


Input

100
1
100000
4
0 100
90 100
100 100
101 100


Output

100
10
0
0


Input

100
5
48 141 231 314 425
7
0 19
50 98
143 30
231 55
342 0
365 100
600 10


Output

19
52
91
10
58
42
100
from bisect import bisect
X=int(input())
K=int(input())
rs=[0]
for r in input().split():
  rs.append(int(r))
A=[[(0,0),(X,X)]]
min_sup=0
max_inf=X
pre_r=0
for i,r in enumerate(rs[1:]):
  d=r-pre_r
  pre_r=r
  m,M=A[-1][0][0],A[-1][1][0]
  if i%2==0:
    if m-d>=0:
      new_m=m-d
    else:
      new_m=0
      min_sup=min_sup+d-m
    if M-d>0:
      new_M=M-d
    else:
      new_M=0
      max_inf=0
  else:
    if M+d<=X:
      new_M=M+d
    else:
      new_M=X
      max_inf=max_inf-(d-(X-M))
    if m+d<X:
      new_m=m+d
    else:
      new_m=X
      min_sup=X
  if new_m==new_M:
    min_sup=X
    max_inf=0             
  A.append([(new_m,min_sup),(new_M,max_inf)])
Q=int(input())
for q in range(Q):
  t,a=map(int,input().split())
  r_num=bisect(rs,t)-1
  m,min_sup=A[r_num][0]
  M,max_inf=A[r_num][1]
  r=rs[r_num]
  if r_num%2==0:
    if a<=min_sup:
      print(max(m-(t-r),0))
    elif min_sup<a<max_inf:
      print(max(m+(a-min_sup)-(t-r),0))
    else:
      print(max(M-(t-r),0))
  else:
    if a<=min_sup:
      print(min(m+(t-r),X))
    elif min_sup<a<max_inf:
      print(min(m+(a-min_sup)+(t-r),X))
    else:
      print(min(M+(t-r),X))
