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.

-----Sample Input-----
180
3
60 120 180
3
30 90
61 1
180 180

-----Sample Output-----
60
1
120

In the first query, 30 out of the initial 90 grams of sand will drop from bulb A, resulting in 60 grams.
In the second query, the initial 1 gram of sand will drop from bulb A, and nothing will happen for the next 59 seconds. Then, we will turn over the sandglass, and 1 second after this, bulb A contains 1 gram of sand at the time in question.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import bisect\noX = int(input())\nK = int(input())\nr= list(map(int,input().split()))\n\n# a X-a\n# min(max(0,a-r[0]))\n#  a-r[0]+r[1]\n\ndef calc_time(t):\n    val = bisect.bisect_left(t,r)\n    diff= t- r[val]\n    return val,diff\n\n\n# [sep1,sep2,a<sep1,sep1<a<sep2,a>sep2  ]\n\nlast =(0,oX,0 ,0,oX)\nres =[last]\nfor i,tr in enumerate(r):\n    sep1,sep2,X,Y,Z=last\n    dt = tr if i==0 else tr-r[i-1]\n    if i%2==0: # a ->b\n\n        X = max(0,X-dt)\n        Y = Y-dt\n        Z = max(0,Z-dt)\n        sep1 = max(sep1,-Y)\n    else: #b-> a\n        X = min(oX,X+dt)\n        Y= Y+dt\n\n        Z = min(oX,Z+dt)\n        sep2 = min(sep2,oX-Y)\n\n    last = (sep1,sep2,X,Y,Z)\n    res.append(last)\n\n#print(res)\n\n\nQ = int(input())\n\nr_index=0\nr.insert(0,0)\nr.append(10000000000)\nfor i in range(Q):\n    def calc(X,r_index,diff):\n        tmp = 1 if r_index%2 else -1\n        return min(oX,max(0,X +tmp* diff))\n    t,a =list(map(int,input().split()))\n    while r[r_index]< t:\n        if r[r_index+1] >t:\n            break\n        r_index+=1\n    sep1, sep2, X, Y, Z = res[r_index]\n    diff = t -r[r_index]\n    #print(t,diff,r_index,r[r_index])\n    if a< sep1:\n        print((calc(X,r_index,diff)))\n    elif a>sep2:\n        print((calc(Z,r_index,diff)))\n    else:\n        print((calc(a+Y,r_index,diff)))\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13877