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        l = len(arr)\n        x = [[] for x in range(l+1)]\n        if l == m:\n            return l\n\n        last = -1\n        lens = [0 for x in range(l+1)]\n        for i in range(0,l):\n            cur = arr[i]\n            right = []\n            left = []\n            if cur+1 < l+1:\n                right = x[cur+1]\n            if cur-1 >= 0:\n                left = x[cur-1]\n\n            lv = rv = cur\n            ss = 1\n            if left:\n                lv = left[1]\n                ss += left[0]\n                lens[left[0]] -=1     \n                if left[0] == m:\n                    last = i\n            if right:\n                rv = right[2]\n                ss += right[0]\n                lens[right[0]] -=1\n                if right[0] == m:\n                    last = i\n            lens[ss]+=1\n            x[lv] = [ss,lv,rv]\n            x[rv] = [ss,lv,rv]\n\n\n        \n        return last\n        \n        for i in range(l-1, 0, -1):\n            cur = arr[i]\n            if lC[cur] or rC[cur]:  return i\n            if cur+m+1 <= l:\n                temp = True\n                for j in range(cur+1,cur+m+1):\n                    if rC[j]:\n                        rC[j] = False\n                        temp = False\n                        break\n                if temp: rC[cur+m+1]=True\n            if cur-m-1 >= 0:\n                temp = True\n                for j in range(cur-m, cur):\n                    if lC[j]: \n                        lC[j] = False\n                        temp = False\n                        break\n                if temp: lC[cur-m-1]=True\n        return -1\n            \n        \n        \n        \n        \n        mx = l\n        mxcount = 1\n        ls = [l]\n        for i in range(l-1,-1,-1):\n            cur = arr[i]\n            prev = 0\n            j = self.bisearch(cur,done,0,len(done))\n            val = done[j]\n            prev = done[j-1]\n\n            if m == val-cur-1 or m == cur-prev-1:\n                return i\n\n            done = done[:j] +[cur] + done[j:]\n            \n            \n        return -1\n    \n    def bisearch(self, cur: List[int], arr:List[int], i:int, j:int) -> int:\n        if i==j:\n            return j\n        if j-i <= 1:\n            if arr[i] < cur:\n                return j\n            else:\n                return i\n        mid = (j-i)//2\n        if cur < arr[i+mid]:\n            return self.bisearch(cur, arr, i, i+mid)\n        else:\n            return self.bisearch(cur, arr, i+mid,j)\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: 6476