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 sys

# sys.stdin = open('f1.in')


def read_int_list():
    return list(map(int, input().split()))


def read_int():
    return int(input())


def read_str_list():
    return input().split()


def read_str():
    return input()


def solve():
    X = read_int()
    K = read_int()
    r = read_int_list()
    Q = read_int()
    j = 0
    sign = -1
    s = 0
    e = X
    y = 0
    origin = 0
    out = [0] * Q
    for i in range(Q):
        t, a = read_int_list()
        while j < K and r[j] < t:
            d = r[j] - origin
            y += d * sign
            if y < 0:
                s += abs(y)
                if s > e:
                    s = e
                y = 0
            if y + e - s > X:
                diff = (y + e - s) - X
                e -= diff
                if e < s:
                    e = s
            if y > X:
                y = X
            origin = r[j]
            j += 1
            sign *= -1
        d = t - origin
        if a <= s:
            res = y
        elif a <= e:
            res = y + a - s
        else:
            res = y + e - s
        res += d * sign
        if res < 0:
            res = 0
        if res > X:
            res = X
        out[i] = res
    return out


def main():
    res = solve()
    print(*res, sep='\n')


if __name__ == '__main__':
    main()
