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#                         # ...0x0... \n#                         y[x] = 1\n#                         dic[x] = x\n#                         if m==1:\n#                             cur_count+=1\n#                     else:\n#                         # ...0x#... \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#                     # ...0x \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#                         # ...#x0... \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#                         # ...#x#... \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[dic[x-1]] = dic[x+1]\n                        \n#                         y[dic[x+1]] = y[x]\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#                     # ...#x \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#         s = [0] * (n+1)\n#         last = -1\n#         cur_count = 0\n#         for idx,x in enumerate(arr):\n#             cur_count=count_cluster(s,x,cur_count)\n#             if cur_count>0:\n#                 last = idx+1\n#         return last\n\n    #gonna try the union-find method\n        def find(parent, x):\n            if x == parent[x]:\n                return x\n            parent[x] = find(parent,parent[x])\n            return parent[x]\n        n = len(arr)\n        parent = [0 for x in range(n+1)]\n        size = [0] * (n+1)\n        count = [0] * (n+1)\n        ans = -1\n        for i,pos in enumerate(arr):\n            \n            size[pos] = 1\n            count[1] += 1\n            parent[pos] = pos\n            for j in [-1,1]:\n                if (pos+j <=n) and (pos+j>0) and (parent[pos+j]!=0):\n                    x = find(parent,pos+j)\n                    y = find(parent,pos)\n                    if x!=y:\n                        \n                        count[size[x]] -=1\n                        count[size[y]] -=1\n                        parent[x] = y\n                        size[y] += size[x]\n                        count[size[y]] +=1\n            if count[m]>0:\n                ans = i+1\n        return ans'
_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: 6640