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
import sys
from bisect import bisect
def input():
	return sys.stdin.readline()[:-1]

x = int(input())
k = int(input())
z = [0] + list(map(int, input().split()))
s = [z[i+1] - z[i] for i in range(k)]

lr = [[0, x]]
pq = [[0, x]]

for i in range(k):
	l, r = lr[-1]
	p, q = pq[-1]
	if i%2 == 0:
		lr.append([max(l-s[i], 0), max(r-s[i], 0)])
		pq.append([min(p + max(min(s[i], x)-l, 0), q), q])
	else:
		lr.append([min(l+s[i], x), min(r+s[i], x)])
		pq.append([p, max(q - max(r-max(x-s[i], 0), 0), p)])

q = int(input())
for _ in range(q):
	t, a = map(int, input().split())
	i = bisect(z, t) - 1
	t -= z[i]
	if a <= pq[i][0]:
		y = lr[i][0]
	elif a >= pq[i][1]:
		y = lr[i][1]
	else:
		y = lr[i][0] + a - pq[i][0]

	if i%2 == 0:
		print(max(y-t, 0))
	else:
		print(min(y+t, x))