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 math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools\n\nsys.setrecursionlimit(10**7)\ninf = 10**20\ngosa = 1.0 / 10**10\nmod = 10**9+7\n\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\ndef LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]\ndef LF(): return [float(x) for x in sys.stdin.readline().split()]\ndef LS(): return sys.stdin.readline().split()\ndef I(): return int(sys.stdin.readline())\ndef F(): return float(sys.stdin.readline())\ndef S(): return input()\n\n\ndef main():\n    x = I()\n    k = I()\n    r = LI()\n    q = I()\n    t = [LI() for _ in range(q)]\n    a = [[0,0,0,x,0,0]]\n    d = 0\n    for i in range(k):\n        c = a[-1][:]\n        rr = r[i] - d\n        d = r[i]\n        if i % 2 == 0:\n            c[1] -= rr\n            c[3] -= rr\n            c[4] -= rr\n            if c[0] > c[1]:\n                c[0] = c[1]\n        else:\n            c[1] += rr\n            c[3] += rr\n            c[4] += rr\n            if c[2] < c[1]:\n                c[2] = c[1]\n        if c[3] > x:\n            c[3] = x\n        if c[3] < 0:\n            c[3] = 0\n        if c[4] > x:\n            c[4] = x\n        if c[4] < 0:\n            c[4] = 0\n\n        c[5] = r[i]\n\n        a.append(c)\n    def bs(i):\n        ma = k\n        mi = 0\n        mm = 0\n        while ma > mi and (ma+mi) // 2 != mm:\n            mm = (ma+mi) // 2\n            if a[mm][5] < i:\n                mi = mm\n            else:\n                ma = mm - 1\n        if a[mm][5] > i:\n            return mm-1\n        if mm == k:\n            return k\n        if a[mm+1][5] <= i:\n            return mm+1\n        return mm\n\n    #print(a)\n    rr = []\n    for c,d in t:\n        ti = bs(c)\n        ai = a[ti]\n        e = x-d\n        #print(c,d,e,ti,ai)\n        if d + ai[0] <= 0:\n            tt = ai[4]\n        elif e - ai[2] <= 0:\n            tt = ai[3]\n        else:\n            tt = d + ai[1]\n        #print('tt',tt)\n        if ti % 2 == 0:\n            tt -= c - ai[5]\n        else:\n            tt += c - ai[5]\n        #print('tt2',tt)\n        if tt < 0:\n            tt = 0\n        elif tt > x:\n            tt = x\n        rr.append(tt)\n\n    return '\\n'.join(map(str,rr))\n\n\nprint((main()))\n\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 178681