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
# coding: utf-8
# Your code here!
import sys
read = sys.stdin.read
readline = sys.stdin.readline


x, = map(int,readline().split())
k, = map(int,readline().split())
*r, = map(int,readline().split())
q, = map(int,readline().split())
r.append(1<<30)

INF = 1<<30
ID_M = (-INF,INF,0)
def compose(lst1,lst2):
    return (funcval(lst1[0],lst2),funcval(lst1[1],lst2),lst1[2]+lst2[2])

def funcval(x,lst):
    a,b,c = lst
    if x <= a-c: return a
    elif x >= b-c: return b
    else: return x+c

#seg = segment_tree_dual(q, compose, funcval, ID_M)
#seg.build([a for a,t,i in ati])

seg = (0,x,0)

tai = []
for i in range(q):
    t,a = map(int,readline().split())
    tai.append((t,a,i))

tai.sort(key=lambda x:x[0])

idx = 0
ans = [0]*q
t0 = 0
coeff = -1
for i,ri in enumerate(r):
    while idx < q and tai[idx][0] < ri:
        t,a,j = tai[idx]
        v = funcval(a,seg)
        ans[j] = min(x,max(v+coeff*(t-t0),0))
        idx += 1
        
    seg = compose(seg,(0,x,coeff*(ri-t0)))
    
    t0 = ri
    coeff *= -1    

    #print(seg)

print(*ans,sep="\n")


