> If you've finished this kata, you can try the [more difficult version](https://www.codewars.com/kata/5b256145a454c8a6990000b5).


## Taking a walk
A promenade is a way of uniquely representing a fraction by a succession of “left or right” choices. 

For example, the promenade `"LRLL"` represents the fraction `4/7`.

Each successive choice (`L` or `R`) changes the value of the promenade by combining the values of the
promenade before the most recent left choice with the value before the most recent right choice. If the value before the most recent left choice was *l/m* and the value before the most recent right choice
was r/s then the new value will be *(l+r) / (m+s)*. 

If there has never been a left choice we use *l=1* and *m=0*;  
if there has never been a right choice we use *r=0* and *s=1*.


So let's take a walk.

* `""` An empty promenade has never had a left choice nor a right choice. Therefore we use *(l=1 and m=0)* and *(r=0 and s=1)*.  
So the value of `""` is *(1+0) / (0+1) = 1/1*.
* `"L"`. Before the most recent left choice we have `""`, which equals *1/1*. There still has never been a right choice, so *(r=0 and s=1)*. So the value of `"L"` is *(1+0)/(1+1) = 1/2*
* `"LR"` = 2/3 as we use the values of `""` (before the left choice) and `"L"` (before the right choice)
* `"LRL"` = 3/5 as we use the values of `"LR"` and `"L"`
* `"LRLL"` = 4/7 as we use the values of `"LRL"` and `"L"` 


Fractions are allowed to have a larger than b.


## Your task

Implement the `promenade` function, which takes an promenade as input (represented as a string), and returns 
the corresponding fraction (represented as a tuple, containing the numerator and the denominator).

```Python
promenade("") == (1,1)
promenade("LR") == (2,3)
promenade("LRLL") == (4,7)
```
```Java
Return the Fraction as an int-Array:
promenade("") == [1,1]
promenade("LR") == [2,3]
promenade("LRLL") == [4,7]
```


*adapted from the 2016 British Informatics Olympiad*

```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 promenade(choices):\n    l, m = (1, 0)\n    r, s = (0, 1)\n    for choice in choices:\n        if choice == 'L': l, m = l+r, m+s\n        elif choice == 'R': r, s = l+r, m+s\n    return l+r,m+s"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'promenade'
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: 5378