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 calc_ans(x):
    if x < 0:
        return 0
    elif x < X:
        return x
    else:
        return X


if __name__ == '__main__':
    # 砂の合計量
    X = int(input())

    # ひっくり返す回数
    K = int(input())
    # ひっくり返す秒数
    r = list(map(int, input().split()))
    # クエリの個数
    Q = int(input())

    # r の制御のための変数
    j = 0
    sign = -1
    s = 0
    e = X
    y = 0
    sand_quantity = [r[0]]
    for i in range(1, K):
        sand_quantity.append(r[i] - r[i - 1])

    chasm_time = 0
    for i in range(Q):
        # t:時刻 a:初期に A に入っている砂の量
        t, a = list(map(int, input().split()))
        while j < K and r[j] < t:
            y += sign * sand_quantity[j]
            # sについて更新
            if y < 0:
                s += -y
                if e < s:
                    s = e
                y = 0
            # eについて更新
            if X < y + e - s:
                tmp_diff = (y + e - s) - X
                e -= tmp_diff
                if e < s:
                    e = s
            if X < y:
                y = X

            chasm_time = r[j]
            j += 1
            sign *= -1

        tmp_time = t - chasm_time

        if a < s:
            ret = y
        elif a < e:
            ret = y + a - s
        else:
            ret = y + e - s

        ret += tmp_time * sign

        print(calc_ans(ret))
        # print("s:" + str(s) + " e:" + str(e) + " y:" + str(y) + " a:" + str(a) + " ret:" + str(ret))
