You have a pointer at index 0 in an array of size arrLen. At each step, you can move 1 position to the left, 1 position to the right in the array or stay in the same place  (The pointer should not be placed outside the array at any time).
Given two integers steps and arrLen, return the number of ways such that your pointer still at index 0 after exactly steps steps.
Since the answer may be too large, return it modulo 10^9 + 7.
 
Example 1:
Input: steps = 3, arrLen = 2
Output: 4
Explanation: There are 4 differents ways to stay at index 0 after 3 steps.
Right, Left, Stay
Stay, Right, Left
Right, Stay, Left
Stay, Stay, Stay

Example 2:
Input: steps = 2, arrLen = 4
Output: 2
Explanation: There are 2 differents ways to stay at index 0 after 2 steps
Right, Left
Stay, Stay

Example 3:
Input: steps = 4, arrLen = 2
Output: 8

 
Constraints:

1 <= steps <= 500
1 <= arrLen <= 10^6

```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 = 'class Solution:\n    # 了解和对比TC\n    # dfs to find all possible way - dfs + dp: cutting rope\n    # state: remaining steps + distance \n        # - break to two parts which sum of remain steps == total steps\n        # - sum of dist <= arrLen\n        # - takes 1 extra steps to connect\n    def numWays(self, steps: int, arrLen: int) -> int:\n        # if dist == 1, combos always 1 regardless of steps\n        if arrLen == 0 or (arrLen == 1 and steps > 0):\n            return arrLen\n        combos = {} # (dist, steps): # of combos\n        def _dfs_ways(steps, arrLen, loc = 0, tar = 0):\n            if steps == 0:\n                return 1 if loc == tar else 0\n            if (steps, loc) in combos: return combos[(steps, loc)]\n            steps -= 1\n            stay = _dfs_ways(steps, arrLen, loc)\n            left = _dfs_ways(steps, arrLen, loc - 1) if loc - 1 >= 0 else 0\n            right = _dfs_ways(steps, arrLen, loc + 1) if loc + 1 < arrLen else 0\n            res = int((left + right + stay) % (math.pow(10, 9) + 7))\n            steps += 1\n            combos[(steps, loc)] = res\n            return res\n        \n        # for i in range(1, min(arrLen, steps // 2) + 1):\n        #     # for combo two parts\n        #     res = 0\n        #     for div in range(1, i + 1): # divide len for dfs\n        #         for left_steps in range(1, steps):\n        #             left_ways = _dfs(left_steps, div)\n        #             right_ways = _dfs(steps - left_steps - 1, i - div)\n        #             res += left_ways * right_ways\n        #     # for whole\n        #     res += _dfs(steps, i)\n        #     combos[(steps, i)] = res\n        _dfs_ways(steps, arrLen)\n        ans = combos[(steps, 0)]\n        return int(ans % (math.pow(10, 9) + 7))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'numWays'
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: 6972