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        dic = {}\n        def count_cluster(y,x,cur_count):\n            length = 0\n            if y[x-1] == 0:\n                if x <n:\n                    if y[x+1] ==0:\n                        y[x] = 1\n                        dic[x] = x\n                        if m==1:\n                            cur_count+=1\n                    else:\n                        oldr = y[x+1]\n                        y[x] = 1 + y[x+1]\n                        y[dic[x+1]] = y[x]\n                        dic[x] = dic[x+1]\n                        dic[dic[x+1]] = x\n                        if oldr == m-1:\n                            cur_count +=1\n                        if oldr == m:\n                            cur_count -=1\n                else:\n                    y[x] = 1\n                    dic[x] = x\n                    if m==1:\n                        cur_count+=1\n            else:\n                if x <n:\n                    if y[x+1] ==0:\n                        oldl = y[x-1]\n                        y[x] = y[x-1] +1\n                        y[dic[x-1]] = y[x]\n                        dic[x] = dic[x-1]\n                        dic[dic[x-1]] = x\n                        if oldl == m-1:\n                            cur_count +=1\n                        if oldl == m:\n                            cur_count -=1\n                    else:\n                        oldr = y[x+1]\n                        oldl = y[x-1]\n                        y[x] = y[x-1] + 1 + y[x+1]\n                        temp = dic[x-1]\n                        \n                        y[dic[x-1]] = y[x]\n                        # dic[x] = dic[x-1]\n                        dic[dic[x-1]] = dic[x+1]\n                        \n                        y[dic[x+1]] = y[x]\n                        # dic[x] = dic[x+1]\n                        dic[dic[x+1]] = temp\n                        \n                        if oldr==m:\n                            cur_count -= 1\n                        if oldl ==m:\n                            cur_count-=1\n                        if oldr+oldl == m-1:\n                            cur_count+=1\n                else:\n                    oldl = y[x-1]\n                    y[x] = y[x-1] +1\n                    y[dic[x-1]] = y[x]\n                    dic[x] = dic[x-1]\n                    dic[dic[x-1]] = x\n                    if oldl == m-1:\n                        cur_count +=1\n                    if oldl == m:\n                        cur_count -=1\n                \n            return cur_count     \n        n = len(arr)\n\n        s = [0] * (n+1)\n        # narr = [(x,idx) for idx, x in enumerate(arr)]\n        # x = sorted(narr,key=lambda x: x[0])\n        last = -1\n        cur_count = 0\n        for idx,x in enumerate(arr):\n            # print(s,idx,x,cur_count)\n            # s[x] = 1\n            cur_count=count_cluster(s,x,cur_count)\n            if cur_count>0:\n                last = idx+1\n        print(last)\n        return last\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: 7250