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 isSorted(self, arr):\n        for i in range(1, len(arr)):\n            if arr[i] < arr[i-1]:\n                return False\n        return True\n    \n    def findLatestStep(self, arr: List[int], m: int) -> int:\n        length = len(arr)\n        if m == length:\n            # Full string of 1s can only be found at last step\n            return m\n        \n        if self.isSorted(arr):\n            return m\n        \n        # Pad front and back to make boundary conditions easier\n        binary = [0] * (len(arr) + 2)\n        latest_step = -1\n        \n        for step in range(length):\n            pos = arr[step]\n            binary[pos] = 1\n            \n            # Examine positions directly to the left and right i.e., group boundaries\n            # Find/store the new group size at the new boundaries\n            left_len = binary[pos-1]\n            right_len = binary[pos+1]\n            new_len = left_len + right_len + 1\n            \n            if left_len == m or right_len == m:\n                # Target length persistent until prev step\n                latest_step = step\n                \n            binary[pos-left_len] = new_len\n            binary[pos+right_len] = new_len\n                \n        return latest_step\n            \n    def findLatestStepNaive2(self, arr: List[int], m: int) -> int:\n        length = len(arr)\n        if m == length:\n            # Full string of 1s can only be found at last step\n            return m\n        \n        if self.isSorted(arr):\n            return m\n        \n        binary = [1] * len(arr)\n        \n        for step in range(length-1, m-1, -1):\n            pos = arr[step] - 1\n            binary[pos] = 0\n            \n            # Note that at each step, only one group is getting split into two\n            # All other groups stay the same, so no need to iterate through entire string\n            left_len = 0\n            right_len = 0\n            for i in range(pos-1, -1, -1):\n                if binary[i]:\n                    left_len += 1\n                else:\n                    break\n            for i in range(pos+1, length):\n                if binary[i]:\n                    right_len += 1\n                else:\n                    break\n            \n            # Check only newly-formed groups.\n            if left_len == m or right_len == m:\n                return step\n        return -1\n\n    def findLatestStepNaive(self, arr: List[int], m: int) -> int:\n        length = len(arr)\n        if m == length:\n            # Full string of 1s can only be found at last step\n            return m\n        \n        if self.isSorted(arr):\n            return m\n        \n        binary = [1] * len(arr)\n        \n        for step in range(length-1, m-1, -1):\n            binary[arr[step] - 1] = 0\n\n            # Iterate through current binary string\n            current_group_len = 0\n            max_group_len = 0\n            for j in range(length):\n                if binary[j]:\n                    current_group_len += 1\n                elif current_group_len > 0:\n                    if current_group_len == m:\n                        return step\n                    max_group_len = max(max_group_len, current_group_len)\n                    current_group_len = 0\n            if current_group_len == m:\n                return step\n            max_group_len = max(max_group_len, current_group_len)\n            # If max drops below m, stop; subsequent passes will only add more 0s\n            if max_group_len < m:\n                return -1\n        return -1'
_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: 5762