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#         n = len(arr)\n#         groups = defaultdict(set)\n#         parents = [i for i in range(n)]\n#         size = [0] * n\n        \n#         def find(node):\n#             if parents[node] == node:\n#                 return node\n#             parent = find(parents[node])\n#             return parent\n        \n#         def union(a, b):\n#             para = find(a)\n#             parb = find(b)\n#             if para != parb:\n#                 groups[parb].update(groups[para])\n#                 groups.pop(para)\n#                 parents[para] = parb\n                \n#         def get_size(a):\n#             parent = find(parents[a])\n#             return len(groups[parent])\n        \n#         def update(i):\n#             check = get_size(i)\n#             sizes[check] -= 1\n#             if sizes[check] == 0:\n#                 sizes.pop(check)\n        \n#         arr = [i-1 for i in arr]\n#         step = 0\n#         ans = -1\n#         sizes = Counter()\n#         for i in arr:\n#             step += 1\n#             size[i] += 1\n#             groups[i].add(i)\n#             sizes[1] += 1\n#             if i-1 >= 0 and i+1 < n and size[i-1] and size[i+1]:\n#                 update(i-1)\n#                 update(i+1)\n#                 update(i)\n#                 union(i, i-1)\n#                 union(i+1, i-1)\n#                 new_size = get_size(i-1)\n#                 sizes[new_size] += 1\n#             elif i-1 >= 0 and size[i-1]:\n#                 update(i-1)\n#                 update(i)\n#                 union(i, i-1)\n#                 new_size = get_size(i-1)\n#                 sizes[new_size] += 1\n#             elif i+1 < n and size[i+1]:\n#                 update(i+1)\n#                 update(i)\n#                 union(i, i+1)\n#                 new_size = get_size(i+1)\n#                 sizes[new_size] += 1\n#             if m in sizes:\n#                 ans = step\n#         return ans\n        N = len(arr)\n        arr = [x - 1 for x in arr]\n        parent = [x for x in range(N)]\n        size = [1 for _ in range(N)]\n        used = [False for _ in range(N)]\n        \n        def ufind(a):\n            if a == parent[a]:\n                return a\n            parent[a] = ufind(parent[a])\n            return parent[a]\n        \n        def uunion(a, b):\n            sa = ufind(a)\n            sb = ufind(b)\n            \n            if sa != sb:\n                parent[sa] = parent[sb]\n                size[sb] += size[sa]\n        \n        def usize(a):\n            return size[ufind(a)]\n            \n        counts = [0] * (N+1)\n        \n        latest = -1\n        for index, x in enumerate(arr):\n            left = 0\n            if x - 1 >= 0 and used[x - 1]:\n                left = usize(x - 1)\n                \n            right = 0\n            if x + 1 < N and used[x + 1]:\n                right = usize(x + 1)\n                \n            current = 1\n            counts[1] += 1\n            if left > 0:\n                counts[left] -= 1\n            if right > 0:\n                counts[right] -= 1\n            counts[1] -= 1\n            used[x] = True\n            \n            new_size = left + right + current\n            #print(x, left, right)\n            counts[new_size] += 1\n            if left > 0:\n                uunion(x, x - 1)\n            if right > 0:\n                uunion(x, x + 1)\n            \n            #print(counts)\n            if counts[m] > 0:\n                latest = max(latest, index + 1)\n        return latest'
_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: 8160