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        if m == len(arr):\n            return len(arr)    \n        \n        u = list(range(len(arr)+1))\n        size = [0] * (len(arr)+1)\n        \n        def find(a):\n            if u[a] != a:\n                u[a] = find(u[a])\n            return u[a]\n        \n        def union(a, b):\n            u1 = find(a)\n            u2 = find(b)\n            if u1 != u2:\n                if size[u1] < size[u2]:\n                    u[u1] = u2\n                    size[u2] += size[u1]\n                else:\n                    u[u2] = u1\n                    size[u1] += size[u2]\n        ans = -1\n        for a_idx, a in enumerate(arr):\n            # print(a)\n            # print(\\"u\\", u)\n            # print(\\"s\\", size)\n            size[a] = 1\n            for i in [a-1, a+1]:\n                if 1 <= i <= len(arr):\n                    if size[find(i)] == m:\n                        ans = a_idx\n                    if size[i] > 0:\n                        union(a, i)\n                    # if size[find(a)] == m:\n                    #     ans = a_idx+1\n                        \n        # print(\\"u\\", u)\n        # print(\\"s\\", size)\n                        \n        for i in range(1, len(arr)+1):\n            # print(i, find(i))\n            if size[find(i)] == m:\n                return len(arr)\n        # print(\\"not last\\")\n        return ans\n        \n#         sections = [\n#             [1, len(arr)]\n#         ]\n#         arr = arr[::-1]\n#         for a_idx, a in enumerate(arr):\n#             # print(a, sections)\n#             l = 0\n#             r = len(sections)\n#             while l < r:\n#                 c = l + (r-l)//2\n#                 if sections[c][0] <= a <= sections[c][1]:\n#                     # a at left\n#                     if a == sections[c][0]:\n#                         sections[c][0] = a+1\n#                         if sections[c][0] > sections[c][1]:\n#                             sections = sections[:c] + sections[c+1:]\n#                         else:\n#                             if sections[c][1] - sections[c][0] + 1 == m:\n#                                 return len(arr) - a_idx - 1 \n#                     elif a == sections[c][1]:\n#                         sections[c][1] = a-1\n#                         if sections[c][0] > sections[c][1]:\n#                             sections = sections[:c] + sections[c+1:]\n#                         else:\n#                             if sections[c][1] - sections[c][0] + 1 == m:\n#                                 return len(arr) - a_idx - 1 \n#                     else:\n#                         tmp = sections[c][1]\n#                         sections[c][1] = a-1\n#                         sections = sections[:c+1] + [[a+1, tmp]] + sections[c+1:]\n#                         # heapq.heappush(sections, [a+1, tmp])\n#                         if sections[c][1] - sections[c][0] + 1 == m:\n#                             return len(arr) - a_idx - 1 \n#                         if sections[c+1][1] - sections[c+1][0] + 1 == m:\n#                             return len(arr) - a_idx - 1\n#                     break   \n#                 elif a < sections[c][0]:\n#                     r = c\n#                 elif a > sections[c][1]:\n#                     l = c+1\n#             # print(sections)\n        \n#         return -1\n        \n#         ans = -1\n#         dp = [0] * (len(arr)+1)\n#         for idx, a in enumerate(arr):\n#             if a > 1:\n#                 dp[a] += dp[a-1]\n#             if a < len(arr):\n#                 dp[a] += dp[a+1]\n#             dp[a] += 1\n#             if dp[a] == m:\n#                 ans = idx+1\n#             print(dp)\n                \n#         return ans\n        \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: 7330