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 = "\ndef main1(x,k,rary,q,ta):\n  aary=[]\n  tary=[]\n  for i,(t,a) in enumerate(ta):\n    aary.append([a,i])\n    tary.append([t,i])\n  tary.sort(key=lambda x:x[0])\n  aary.sort(key=lambda x:x[0])\n  l,r=0,x # [l,r]:0,xの壁にぶつかっていない初期aの範囲\n  lt,rt=-1,-1 # 壁ぶつかりが発生したあと砂時計がひっくり返る時間\n  tidx=0\n  nowt=0\n  nowu='A'\n  da=0\n  ret=[-1]*q\n  daary={}\n  rary.append(10**9+1)\n  k+=1\n  for i,ri in enumerate(rary):\n    while tidx<q and tary[tidx][0]<=ri:\n      t,j=tary[tidx]\n      tidx+=1\n      a=ta[j][1]\n      if nowu=='A':\n        if l<=a<=r:\n          ret[j]=a+da-(t-nowt)\n        elif a<l:\n          ret[j]=da-daary[lt]-(t-nowt)\n        else:\n          ret[j]=x+da-daary[rt]-(t-nowt)\n      else:\n        if l<=a<=r:\n          ret[j]=a+da+(t-nowt)\n        elif a<l:\n          ret[j]=da-daary[lt]+(t-nowt)\n        else:\n          ret[j]=x+da-daary[rt]+(t-nowt)\n      ret[j]=max(0,ret[j])\n      ret[j]=min(x,ret[j])\n    if nowu=='A':\n      dt=ri-nowt\n      da-=dt\n      if l<-da:\n        l=-da\n        lt=ri\n      nowt=ri\n      nowu='B'\n    else:\n      dt=ri-nowt\n      da+=dt\n      if r>x-da:\n        r=x-da\n        rt=ri\n      nowt=ri\n      nowu='A'\n    daary[nowt]=da\n    if l>=r:\n      if nowu=='B':\n        da=0\n      else:\n        da=x\n      for ii in range(i+1,k):\n        ri=rary[ii]\n        while tidx<q and tary[tidx][0]<=ri:\n          t,j=tary[tidx]\n          tidx+=1\n          if nowu=='A':\n            ret[j]=da-(t-nowt)\n          else:\n            ret[j]=da+(t-nowt)\n          ret[j]=max(0,ret[j])\n          ret[j]=min(x,ret[j])\n        if nowu=='A':\n          da-=ri-nowt\n          da=max(da,0)\n          nowu='B'\n        else:\n          da+=ri-nowt\n          da=min(da,x)\n          nowu='A'\n        nowt=ri\n      break\n  return ret\n\nimport sys\ninput=sys.stdin.readline\ndef __starting_point():\n  x=int(input())\n  k=int(input())\n  r=list(map(int,input().split()))\n  q=int(input())\n  ta=[list(map(int,input().split())) for _ in range(q)]\n  print(*main1(x,k,r,q,ta),sep='\\n')\n\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13783