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
def main():
    import sys
    from operator import itemgetter
    input = sys.stdin.readline

    X = int(input())
    K = int(input())
    R = list(map(int, input().split()))
    Q = []
    for r in R:
        Q.append((r, -1))
    q = int(input())
    for _ in range(q):
        t, a = map(int, input().split())
        Q.append((t, a))
    Q.sort(key=itemgetter(0))

    #print(Q)
    prev = 0
    m = 0
    M = X
    flg = -1
    R_cs = 0
    for t, a in Q:
        if a < 0:
            r = t - prev
            R_cs -= r * flg
            if flg == -1:
                m = max(0, m-r)
                M = max(0, M-r)
                flg = 1
            else:
                m = min(X, m+r)
                M = min(X, M+r)
                flg = -1
            prev = t
        else:
            if m == M:
                if flg == 1:
                    print(min(X, m + t - prev))
                else:
                    print(max(0, m - t + prev))
            else:
                am = m + R_cs
                aM = M + R_cs
                #print('am', am, 'aM', aM, m, M)
                if a <= am:
                    if flg == 1:
                        print(min(X, m + t - prev))
                    else:
                        print(max(0, m - t + prev))
                elif a >= aM:
                    if flg == 1:
                        print(min(X, M + t - prev))
                    else:
                        print(max(0, M - t + prev))
                else:
                    if flg == 1:
                        print(min(X, m + (a - am) + t - prev))
                    else:
                        print(max(0, m + (a - am) - t + prev))


if __name__ == '__main__':
    main()
