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
import bisect
def inpl(): return [int(i) for i in input().split()]

X = int(input())
K = int(input())
r = [0] + inpl()
stu = [()]*(K+1)
stu[0] = (X, 0, 0)
for i, v in enumerate(r[1:], 1):
    s, t, u = stu[i-1]
    if i%2:
        rs = r[i-1] - r[i]
        ap = - rs - t
        if ap >= s:
            stu[i] = 0, 0, 0
        elif ap >= u:
            stu[i] = s, t+rs, ap
        else:
            stu[i] = s, t+rs, u
    else:
        rs = r[i] - r[i-1]
        ap = X - rs - t
        if ap >= s:
            stu[i] = s, t+rs, u
        elif ap >= u:
            stu[i] = ap, t+rs, u
        else:
            stu[i] = X, 0, X
Q = int(input())
for _ in range(Q):
    ti, a = inpl()
    x = bisect.bisect_right(r, ti)
    ti -= r[x-1]
    s, t, u = stu[x-1]
    if a >= s:
        R = s + t
    elif a >= u:
        R = a + t
    else:
        R = u + t
    if x % 2:
        print(max(0, R - ti))
    else:
        print(min(X, R + ti))