There is a special square room with mirrors on each of the four walls.  Except for the southwest corner, there are receptors on each of the remaining corners, numbered 0, 1, and 2.
The square room has walls of length p, and a laser ray from the southwest corner first meets the east wall at a distance q from the 0th receptor.
Return the number of the receptor that the ray meets first.  (It is guaranteed that the ray will meet a receptor eventually.)
 

Example 1:
Input: p = 2, q = 1
Output: 2
Explanation: The ray meets receptor 2 the first time it gets reflected back to the left wall.


Note:

1 <= p <= 1000
0 <= q <= p

```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

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "from fractions import Fraction as F\n\nclass Solution:\n    def mirrorReflection(self, p: int, q: int) -> int:\n        def line_y(x: int, x_0:int, y_0:int, d_x: int, d_y: int) -> int:\n            '''\n                Return the y coordinate of given x for the line defined by (x_0, y_0) and (d_x, d_y)\n            '''\n            return F(d_y, d_x) * (x - x_0) + y_0\n        \n        def line_x(y: int, x_0: int, y_0: int, d_x: int, d_y: int) -> int:\n            '''\n                Return the x coordinate of given y for the line defined by (x_0, y_0) and (d_x, d_y)\n            '''\n            return (y - y_0) / F(d_y, d_x) + x_0\n            \n        # (x, y) start position of the ray\n        # (d_x, d_y) direction of the ray\n        x_0, y_0, d_x, d_y = 0, 0, p, q\n        \n        while True:\n            if d_x > 0:\n                # Toward right                \n                y_intercept_right = line_y(p, x_0, y_0, d_x, d_y)\n\n                if y_intercept_right == p:\n                    return 1\n                elif y_intercept_right == 0:\n                    return 0\n                elif 0 < y_intercept_right < p:\n                    # hit right\n                    x_0, y_0, d_x, d_y = p, y_intercept_right, -d_x, d_y\n                elif y_intercept_right > p:\n                    # hit top\n                    x_0, y_0, d_x, d_y = line_x(p, x_0, y_0, d_x, d_y), p, d_x, -d_y\n                else:\n                    # y_intercept_right < 0\n                    # hit bottom\n                    x_0, y_0, d_x, d_y = line_x(0, x_0, y_0, d_x, d_y), 0, d_x, -d_y\n            else:\n                # Toward left\n                y_intercept_left = line_y(0, x_0, y_0, d_x, d_y)\n\n                if y_intercept_left == p:\n                    return 2\n                elif 0 < y_intercept_left < p:\n                    # hit left\n                    x_0, y_0, d_x, d_y = 0, y_intercept_left, -d_x, d_y\n                elif y_intercept_left > p:\n                    # hit top\n                    x_0, y_0, d_x, d_y = line_x(p, x_0, y_0, d_x, d_y), p, d_x, -d_y\n                else:\n                    # y_intercept_left < 0\n                    # hit bottom\n                    x_0, y_0, d_x, d_y = line_x(0, x_0, y_0, d_x, d_y), 0, d_x, -d_y"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'mirrorReflection'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 11573