# Task
 You're standing at the top left corner of an `n × m` grid and facing towards the `right`. 
 
 Then you start walking one square at a time in the direction you are facing. 
 
 If you reach the border of the grid or if the next square you are about to visit has already been visited, you turn right. 
 
 You stop when all the squares in the grid are visited. What direction will you be facing when you stop?

 You can see the example of your long walk in the image below. The numbers denote the order in which you visit the cells.

 ![](https://i.gyazo.com/2fc5884d2c227a0ddeca503e6a0261be.png)

 Given two integers n and m, denoting the number of rows and columns respectively, find out the direction you will be facing at the end. 
 
 Output `"L"` for left, `"R"` for right, `"U"` for up, and `"D"` for down.

# Example:

 For `n = 3, m = 3`, the output should be `"R"`.

 This example refers to the picture given in the description. At the end of your walk you will be standing in the middle of the grid facing right.

# Input/Output


 - `[input]` integer `n`
 
 number of rows.

 `1 <= n <= 1000`


 - `[input]` integer `m`
 
 number of columns.

 `1 <= m <= 1000`
 
 
 - `[output]` a string

 The final direction.

```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 = "NEXT = {'R': 'D', 'D': 'L', 'L': 'U', 'U': 'R'}\n\ndef direction_in_grid(n, m, d='R'):\n    while n > 1:\n        n, m, d = m, n-1, NEXT[d]\n    return d"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'direction_in_grid'
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: 5330