Given an array arr that represents a permutation of numbers from 1 to n. You have a binary string of size n that initially has all its bits set to zero.
At each step i (assuming both the binary string and arr are 1-indexed) from 1 to n, the bit at position arr[i] is set to 1. You are given an integer m and you need to find the latest step at which there exists a group of ones of length m. A group of ones is a contiguous substring of 1s such that it cannot be extended in either direction.
Return the latest step at which there exists a group of ones of length exactly m. If no such group exists, return -1.
 
Example 1:
Input: arr = [3,5,1,2,4], m = 1
Output: 4
Explanation:
Step 1: "00100", groups: ["1"]
Step 2: "00101", groups: ["1", "1"]
Step 3: "10101", groups: ["1", "1", "1"]
Step 4: "11101", groups: ["111", "1"]
Step 5: "11111", groups: ["11111"]
The latest step at which there exists a group of size 1 is step 4.
Example 2:
Input: arr = [3,1,5,4,2], m = 2
Output: -1
Explanation:
Step 1: "00100", groups: ["1"]
Step 2: "10100", groups: ["1", "1"]
Step 3: "10101", groups: ["1", "1", "1"]
Step 4: "10111", groups: ["1", "111"]
Step 5: "11111", groups: ["11111"]
No group of size 2 exists during any step.

Example 3:
Input: arr = [1], m = 1
Output: 1

Example 4:
Input: arr = [2,1], m = 2
Output: 2

 
Constraints:

n == arr.length
1 <= n <= 10^5
1 <= arr[i] <= n
All integers in arr are distinct.
1 <= m <= arr.length

```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    def findLatestStep(self, arr: List[int], m: int) -> int:\n        \n        \n        \n        # my solution ... 1424 ms ... 77 % ... 27.7 MB ... 92 %\n        #  time: O(n)\n        # space: O(n)\n        \n        res = -1\n        e2s = {}  # e2s[5] = 3 表示 3-4-5 位置现在均为1。此时必有s2e[3] = 5\n        s2e = {}\n        cnt = {}  # cnt[3] = 8 表示此时有 8 个 '111'\n        for i, v in enumerate(arr):  # i+1 是当前 step，v是当前step从0变为1的位置，其两侧的索引为v-1和v+1\n            if v-1 not in e2s and v+1 not in s2e:\n                l, r = v, v\n            elif v-1 not in e2s and v+1 in s2e:\n                l, r = v, s2e[v+1]\n                del s2e[v+1]\n                cnt[r-v] -= 1\n                if not cnt[r-v]:\n                    del cnt[r-v]\n            elif v-1 in e2s and v+1 not in s2e:\n                l, r = e2s[v-1], v\n                del e2s[v-1]\n                cnt[v-l] -= 1\n                if not cnt[v-l]:\n                    del cnt[v-l]\n            else:\n                l, r = e2s[v-1], s2e[v+1]  # 位置 v 变为 1 后，v 左侧最远 1 及 v 右侧最远 1\n                del e2s[v-1]\n                del s2e[v+1]\n                cnt[v-l] -= 1  # 更新旧的频次\n                if not cnt[v-l]:\n                    del cnt[v-l]\n                cnt[r-v] -= 1\n                if not cnt[r-v]:\n                    del cnt[r-v]\n            s2e[l] = r\n            e2s[r] = l\n            cnt[r-l+1] = cnt.get(r-l+1, 0) + 1  # 增加新的频次\n            if m in cnt:\n                res = i + 1\n        return res\n        \n        \n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'findLatestStep'
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: 6328