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
#!/usr/bin/env python3
import bisect

def main():
    X = int(input())
    K = int(input())
    r = list(map(int, input().split()))
    Q = int(input())
    q_list = []
    for i in range(Q):
        q_list.append(list(map(int, input().split())))

    r = [0] + r
    a = [0]
    upper_limit = [X]
    lower_limit = [0]

    x, ux, lx = 0, X, 0
    for i in range(1, K + 1):
        diff = r[i] - r[i - 1]
        if i % 2 == 1:
            x -= diff
            ux -= diff
            ux = max(ux, 0)
            lx -= diff
            lx = max(lx, 0)
        else:
            x += diff
            ux += diff
            ux = min(ux, X)
            lx += diff
            lx = min(lx, X)
        a.append(x)
        upper_limit.append(ux)
        lower_limit.append(lx)

    asc_i = [0]
    dsc_i = [1]
    x = 0
    for i in range(2, K + 1, 2):
        if x < a[i]:
            x = a[i]
            asc_i.append(i)
    x = a[1]
    for i in range(3, K + 1, 2):
        if a[i] < x:
            x = a[i]
            dsc_i.append(i)

    asc_a = [a[i] for i in asc_i]
    dsc_a = [-a[i] for i in dsc_i]


    for [t, a0] in q_list:
        ri = bisect.bisect_right(r, t) - 1

        ui = bisect.bisect_left(asc_a, X - a0)
        li = bisect.bisect_left(dsc_a, a0)

        ai, di = None, None
        if ui < len(asc_i):
            ai = asc_i[ui]
            if ri < ai:
                ai = None
        if li < len(dsc_i):
            di = dsc_i[li]
            if ri < di:
                di = None

        d = 0
        if (not ai is None) or (not di is None):
            if ai is None:
                d = -1
            elif di is None:
                d = 1
            else:
                d = 1 if ai < di else -1

        x = a0 + a[ri]
        if d == 1:
            x = upper_limit[ri]
        elif d == -1:
            x = lower_limit[ri]
        x += (t - r[ri]) * (-1 if ri % 2 == 0 else 1)
        x = min(max(x, 0), X)

        print(x)

if __name__ == '__main__':
    main()

