## **Task**

Four mirrors are placed in a way that they form a rectangle with corners at coordinates `(0, 0)`, `(max_x, 0)`, `(0, max_y)`, and `(max_x, max_y)`. A light ray enters this rectangle through a hole at the position `(0, 0)` and moves at an angle of 45 degrees relative to the axes. Each time it hits one of the mirrors, it gets reflected. In the end, the light ray hits one of the rectangle's corners, and flies out. Your function must determine whether the exit point is either `(0, 0)` or `(max_x, max_y)`. If it is either `(0, 0)` or `(max_x, max_y)`, return `True` and `False` otherwise.

**Example**

For `max_x = 10` and `max_y = 20`, the ray goes through the following lattice points: `(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (7, 7), (8, 8), (9, 9), (10, 10), (9, 11), (8, 12), (7, 13), (6, 14), (5, 15), (4, 16), (3, 17), (2, 18), (1, 19), (0, 20)`.

The ray left the rectangle at position `(0, 20)`, so the result is `False`.

Here is an image of the light being reflected.
![d](https://upload.wikimedia.org/wikipedia/commons/thumb/7/73/Arithmetic-billiard-40-10.jpg/450px-Arithmetic-billiard-40-10.jpg)


Also, once completing this kata, please do not rate it based off of the difficulty level(kyu) and instead on whether you think it is a good kata.

```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 math import gcd\n\ndef reflections(x,y):\n    v   = gcd(x,y)\n    x,y = x//v, y//v\n    return not( x&1 ^ y&1 )'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'reflections'
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: 5338