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
# F
# input
from bisect import bisect
X = int(input())
K = int(input())
r_list = [0] + list(map(int, input().split()))

Q = int(input())
query_list = [list(map(int, input().split())) for _ in range(Q)]


MmRL_list = []

# M:max, m:min, R:min_a(M), L:max_a(m)
M = X
m = 0
R = X
L = 0

MmRL_list.append([M, m, R, L])

for i in range(K):
    M_ = M
    m_ = m
    R_ = R
    L_ = L
    lag = r_list[i+1] - r_list[i]
    # update
    if i % 2 == 0:
        if M_ - lag < 0:
            M = 0
            R = 0
        else:
            M = M_ - lag
            R = R_
        if m_ - lag < 0:
            m = 0
            L = L_ + lag - m_
        else:
            m = m_ - lag
            L = L_
    else:
        if M_ + lag > X:
            M = X
            R = R_ - (M_ + lag - X)
        else:
            M = M_ + lag
            R = R_
        if m_ + lag > X:
            m = X
            L = X
        else:
            m = m_ + lag
            L = L_
    MmRL_list.append([M, m, R, L])
        

# print(MmRL_list)
for q in range(Q):
    t, a = query_list[q]
    j = bisect(r_list, t) - 1
    # find status then
    M, m, R, L = MmRL_list[j]
    if a <= L:
        a_ = m
    elif a >= R:
        a_ = M
    else:
        a_ = m + (a - L)
    t_ = t - r_list[j]
    if j % 2 == 0:
        res = max(a_ - t_, 0)
    else:
        res = min(a_ + t_, X)
    print(res)
