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 = 'X=int(input())\nK=int(input())\nr=list(map(int,input().split()))\nQ=int(input())\np=[tuple(map(int,input().split())) for i in range(Q)]\n\nN=Q\nL=0\nR=Q-1\nstart=0\nsign="-"\n\n# N: 処理する区間の長さ\n\nN0 = 2**(N-1).bit_length()\ndata = [0]*(2*N0)\nINF = 0\n# 区間[l, r+1)の値をvに書き換える\n# vは(t, value)という値にする (新しい値ほどtは大きくなる)\ndef update(l, r, v):\n    L = l + N0; R = r + N0\n    while L < R:\n        if R & 1:\n            R -= 1\n            data[R-1] += v\n\n        if L & 1:\n            data[L-1] += v\n            L += 1\n        L >>= 1; R >>= 1\n# a_iの現在の値を取得\ndef query(k):\n    k += N0-1\n    s = INF\n    while k >= 0:\n        s += data[k]\n        k = (k - 1) // 2\n    return s\n\nq=[]\nfor i in range(Q):\n    t,a=p[i]\n    p[i]=(a,t,i)\n\np.sort()\ndic=[-1]*Q\nfor i in range(Q):\n    a,t,id=p[i]\n    update(i,i+1,a)\n    dic[id]=i\n    q.append((t,id,0))\n\nfor i in range(K):\n    q.append((r[i],-1,r[i]-r[i-1]*(i>0)))\n\nq.sort()\nans=[0]*Q\nfor val,id,c in q:\n    if id==-1:\n        if sign=="-":\n            update(L,R+1,-c)\n            while query(L+1)<0 and L<R:\n                L+=1\n            a=query(L)\n            if a<0:\n                update(L,L+1,-a)\n            start=val\n            sign="+"\n        else:\n            update(L,R+1,c)\n            while query(R-1)>X and L<R:\n                R-=1\n            a=query(R)\n            if a>X:\n                update(R,R+1,X-a)\n            start=val\n            sign="-"\n    else:\n        pid,id=id,dic[id]\n        if sign=="-":\n            if id<L:\n                res=max(query(L)-(val-start),0)\n            elif id>R:\n                res=max(query(R)-(val-start),0)\n            else:\n                res=max(query(id)-(val-start),0)\n        else:\n            if id<L:\n                res=min(query(L)+(val-start),X)\n            elif id>R:\n                res=min(query(R)+(val-start),X)\n            else:\n                res=min(query(id)+(val-start),X)\n        ans[pid]=res\n\n\nfor i in range(Q):\n    print((ans[i]))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14535