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        bit_to_parent = [-1] * len(arr)\n        size = [0] * len(arr)\n        last_step = -1\n        groups_of_size_m = 0\n\n        def root(bit):\n            if bit_to_parent[bit] == -1:\n                return -1\n\n            root = bit\n            while root != bit_to_parent[root]:\n                root = bit_to_parent[root]\n            \n            curr = bit\n            while curr != root:\n                tmp = bit_to_parent[bit]\n                bit_to_parent[bit] = root\n                curr = tmp\n\n            # print(\\"root\\", bit, root)\n            return root\n        \n        def union(b1, b2):\n            # print(\\"union\\", b1, b2)\n            nonlocal size\n            nonlocal groups_of_size_m\n            \n            if b1 == b2:\n                size[b1] = 1\n                if m == 1:\n                    groups_of_size_m += 1\n                return\n            \n            root_b1 = root(b1)\n            root_b2 = root(b2)\n            \n            if root_b1 == -1 or root_b2 == -1:\n                # Can\'t union\n                return\n            \n            if size[root_b1] >= size[root_b2]:\n                parent = root_b1\n                child = root_b2\n            else:\n                parent = root_b2\n                child = root_b1\n            \n            old_parent_size = size[parent]\n            old_child_size = size[child]\n            \n            size[parent] += size[child]\n            bit_to_parent[child] = parent\n            \n            # print(\\"union\\", b1, b2, parent, child, old_parent_size, old_child_size, size[parent])\n            if old_parent_size == m:\n                groups_of_size_m -= 1\n            \n            if old_child_size == m:\n                groups_of_size_m -= 1\n            \n            if size[parent] == m:\n                groups_of_size_m += 1\n            \n            return parent\n        \n        for i in range(len(arr)):\n            bit = arr[i] - 1\n            bit_to_parent[bit] = bit\n            \n            union(bit, bit)\n            if bit - 1 >= 0:\n                union(bit, bit - 1)\n            if bit + 1 < len(arr):\n                union(bit, bit + 1)\n            \n            if groups_of_size_m > 0:\n                last_step = i + 1\n        \n        return last_step'
_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: 6958