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
X = int(input())
K = int(input())
R = [int(x) for x in reversed(input().split())]
for i in range(0,K-1): R[i] -= R[i+1]
Q = int(input())

aM = X
M = X
am = 0
m = 0
now = 0
sign = -1
timer = R.pop()

def Go(time):
    global aM,M,am,m
    if sign==1:
        if m+time>X:
            m = X
            M = X
            aM = am
        elif M+time>X:
            m += time
            M = X
            aM = am + M - m
        else:
            m += time
            M += time
    else:
        if M-time<0:
            m = 0
            M = 0
            am = aM
        elif m-time<0:
            m = 0
            M -= time
            am = aM + m - M
        else:
            m -= time
            M -= time

for i in range(Q):
    t,a = [int(x) for x in input().split()]
    t -= now
    now += t
    
    while t>=timer:
        Go(timer)
        t -= timer
        if R:
            timer = R.pop()
        else:
            timer = float("inf")
        sign *= -1
    
    Go(t)
    timer -= t
    
    if a<am:
        print(m)
    elif a>aM:
        print(M)
    else:
        print(m+a-am)