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_lst = [int(_) for _ in input().split()]\nQ = int(input())\nt_lst, a_lst = [], []\nfor i in range(Q):\n    buf = input().split()\n    t_lst.append(int(buf[0]))\n    a_lst.append(int(buf[1]))\n    \npos_lst = []\nfor i, r in enumerate(r_lst):\n    direc = "+" if i%2==0 else "-"\n    pos_lst.append((r, direc))\nfor i, t in enumerate(t_lst):\n    pos_lst.append((t, i))\npos_lst = sorted(pos_lst, key=lambda tup: tup[0])\n\n\nleft, right  = 0, X\nval = [0, 0, X] \n\ndirec = "-"\nprv = 0\nfor pos in pos_lst:\n#    print(left, right)\n#    print(val)\n#    print(pos)\n#    print()\n    \n    elapsed = pos[0] - prv\n    prv = pos[0]\n    \n    if direc == "+":\n        val[0] = min(X, val[0] + elapsed)\n        val[1] += elapsed\n        val[2] = min(X, val[2] + elapsed)\n        right = min(right, X - val[1])\n    else:\n        val[0] = max(0, val[0] - elapsed)\n        val[1] -= elapsed\n        val[2] = max(0, val[2] - elapsed)     \n        left = max(left, -(val[1]))\n        \n    if pos[1] == "+" or pos[1] == "-":\n        direc = pos[1]\n    else: #is query\n        a = a_lst[pos[1]]\n        \n        if a <= left:\n            print(val[0])\n        elif a >= right:\n            print(val[2])\n        else:\n            print( a + val[1])'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14041