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 = '#!/usr/bin/env python3\nimport bisect\n\ndef main():\n    X = int(input())\n    K = int(input())\n    r = list(map(int, input().split()))\n    Q = int(input())\n    q_list = []\n    for i in range(Q):\n        q_list.append(list(map(int, input().split())))\n\n    r = [0] + r\n    a = [0]\n    upper_limit = [X]\n    lower_limit = [0]\n\n    x, ux, lx = 0, X, 0\n    for i in range(1, K + 1):\n        diff = r[i] - r[i - 1]\n        if i % 2 == 1:\n            x -= diff\n            ux -= diff\n            ux = max(ux, 0)\n            lx -= diff\n            lx = max(lx, 0)\n        else:\n            x += diff\n            ux += diff\n            ux = min(ux, X)\n            lx += diff\n            lx = min(lx, X)\n        a.append(x)\n        upper_limit.append(ux)\n        lower_limit.append(lx)\n\n    asc_i = [0]\n    dsc_i = [1]\n    x = 0\n    for i in range(2, K + 1, 2):\n        if x < a[i]:\n            x = a[i]\n            asc_i.append(i)\n    x = a[1]\n    for i in range(3, K + 1, 2):\n        if a[i] < x:\n            x = a[i]\n            dsc_i.append(i)\n\n    asc_a = [a[i] for i in asc_i]\n    dsc_a = [-a[i] for i in dsc_i]\n\n\n    for [t, a0] in q_list:\n        ri = bisect.bisect_right(r, t) - 1\n\n        ui = bisect.bisect_left(asc_a, X - a0)\n        li = bisect.bisect_left(dsc_a, a0)\n\n        ai, di = None, None\n        if ui < len(asc_i):\n            ai = asc_i[ui]\n            if ri < ai:\n                ai = None\n        if li < len(dsc_i):\n            di = dsc_i[li]\n            if ri < di:\n                di = None\n\n        d = 0\n        if (not ai is None) or (not di is None):\n            if ai is None:\n                d = -1\n            elif di is None:\n                d = 1\n            else:\n                d = 1 if ai < di else -1\n\n        x = a0 + a[ri]\n        if d == 1:\n            x = upper_limit[ri]\n        elif d == -1:\n            x = lower_limit[ri]\n        x += (t - r[ri]) * (-1 if ri % 2 == 0 else 1)\n        x = min(max(x, 0), X)\n\n        print(x)\n\ndef __starting_point():\n    main()\n\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15571