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
X = int(input())
K = int(input())
r_lst = [int(_) for _ in input().split()]
Q = int(input())
t_lst, a_lst = [], []
for i in range(Q):
    buf = input().split()
    t_lst.append(int(buf[0]))
    a_lst.append(int(buf[1]))
    
pos_lst = []
for i, r in enumerate(r_lst):
    direc = "+" if i%2==0 else "-"
    pos_lst.append((r, direc))
for i, t in enumerate(t_lst):
    pos_lst.append((t, i))
pos_lst = sorted(pos_lst, key=lambda tup: tup[0])


left, right  = 0, X
val = [0, 0, X] 

direc = "-"
prv = 0
for pos in pos_lst:
#    print(left, right)
#    print(val)
#    print(pos)
#    print()
    
    elapsed = pos[0] - prv
    prv = pos[0]
    
    if direc == "+":
        val[0] = min(X, val[0] + elapsed)
        val[1] += elapsed
        val[2] = min(X, val[2] + elapsed)
        right = min(right, X - val[1])
    else:
        val[0] = max(0, val[0] - elapsed)
        val[1] -= elapsed
        val[2] = max(0, val[2] - elapsed)     
        left = max(left, -(val[1]))
        
    if pos[1] == "+" or pos[1] == "-":
        direc = pos[1]
    else: #is query
        a = a_lst[pos[1]]
        
        if a <= left:
            print(val[0])
        elif a >= right:
            print(val[2])
        else:
            print( a + val[1])