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
input = __import__('sys').stdin.readline
MIS = lambda: map(int,input().split())
 
# f(a) = z                 a <= x1
#        a+z-x1      x1 <= a <= x2
#        x2+z-x1     x2 <= a
class Sandgraph:
    def __init__(_, X):
        _.z = _.x1 = 0
        _.x2 = X
    
    def add(_, dt):
        # Go towards the ceiling
        d1 = min(dt, X-(_.x2+_.z-_.x1))
        _.z+= d1
        dt-= d1
        # Reduce the diagonal
        d1 = min(dt, _.x2-_.x1)
        _.z+= d1
        _.x2-= d1
    
    def sub(_, dt):
        # Go towards the floor
        d1 = min(dt, _.z)
        _.z-= d1
        dt-= d1
        # Reduce the diagonal
        d1 = min(dt, _.x2-_.x1)
        _.x1+= d1
    
    def __call__(_, a):
        if a <= _.x1: return _.z
        elif a <= _.x2: return a + _.z - _.x1
        else: return _.x2 + _.z - _.x1
 
X = int(input())
k = int(input())
rev = list(MIS())
Q = int(input())
sand = Sandgraph(X)
 
last_t = 0
i = 0 # even -, odd +
for QUERY in range(Q):
    t, a = MIS()
    while i<k and rev[i] <= t:
        dt = rev[i] - last_t
        if i%2 == 0: sand.sub(dt)
        else: sand.add(dt)
        last_t = rev[i]
        i+= 1
    dt = t - last_t
    if i%2 == 0: sand.sub(dt)
    else: sand.add(dt)
    print(sand(a))
    last_t = t