# Task
 In ChessLand there is a small but proud chess bishop with a recurring dream. 
 
 In the dream the bishop finds itself on an `n × m` chessboard with mirrors along each edge, and it is not a bishop but a ray of light. This ray of light moves only along diagonals (the bishop can't imagine any other types of moves even in its dreams), it never stops, and once it reaches an edge or a corner of the chessboard it reflects from it and moves on.

 Given the initial position and the direction of the ray, find its position after `k` steps where a step means either moving from one cell to the neighboring one or reflecting from a corner of the board.

# Example

 For `boardSize = [3, 7], initPosition = [1, 2], initDirection = [-1, 1] and k = 13,` the output should be `[0, 1]`.

 Here is the bishop's path:
```
[1, 2] -> [0, 3] -(reflection from the top edge)
         -> [0, 4] -> [1, 5] -> [2, 6] -(reflection from the bottom right corner)
         -> [2, 6] ->[1, 5] -> [0, 4] -(reflection from the top edge)
         -> [0, 3] ->[1, 2] -> [2, 1] -(reflection from the bottom edge)
         -> [2, 0] -(reflection from the left edge)
         -> [1, 0] -> [0, 1]```

 ![](https://codefightsuserpics.s3.amazonaws.com/tasks/chessBishopDream/img/example.png?_tm=1472324389202)

# Input/Output


 - `[input]` integer array `boardSize`

    An array of two integers, the number of `rows` and `columns`, respectively. Rows are numbered by integers from `0 to boardSize[0] - 1`, columns are numbered by integers from `0 to boardSize[1] - 1` (both inclusive).

    Constraints: `1 ≤ boardSize[i] ≤ 20.`


 - `[input]` integer array `initPosition`

    An array of two integers, indices of the `row` and the `column` where the bishop initially stands, respectively.

    Constraints:  `0 ≤ initPosition[i] < boardSize[i]`.


 - `[input]` integer array `initDirection`

    An array of two integers representing the initial direction of the bishop. 
    
    If it stands in `(a, b)`, the next cell he'll move to is `(a + initDirection[0], b + initDirection[1])` or whichever it'll reflect to in case it runs into a mirror immediately.

    Constraints: `initDirection[i] ∈ {-1, 1}`.


 - `[input]` integer `k`

    Constraints: `1 ≤ k ≤ 1000000000`.


 - `[output]` an integer array

    The position of the bishop after `k` steps.

```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 = 'def chess_bishop_dream(bs, init_pos, init_dir, k):\n    \n    pos, dir = init_pos[:], init_dir[:]\n    n, start = k, (init_pos, init_dir)\n    while n:\n        pos = [x+dx for x,dx in zip(pos, dir)]\n        for i in range(2):\n            if not (0 <= pos[i] < bs[i]):\n                dir[i] *= -1\n                pos[i] = [0, bs[i]-1][ pos[i]>0 ]\n        n -= 1\n        if start == (pos, dir): n %= k-n\n        \n    return pos'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'chess_bishop_dream'
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: 6092