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 UF:\n    def __init__(self, n):\n        self.arr = list(range(n + 1))\n        self.rank = [1] * n\n        \n    def root(self, x): \n        curr = x    \n        while curr != self.arr[curr]:\n            curr = self.arr[curr]\n    \n        return curr\n    \n    def union(self, x, y):\n        root_x = self.root(x)\n        root_y = self.root(y)\n        \n        if root_x == root_y:\n            return\n        \n        rank_x = self.rank[root_x]\n        rank_y = self.rank[root_y]\n\n        if rank_x >= rank_y:\n            self.arr[root_y] = root_x\n            self.rank[root_x] += rank_y\n        else:\n            self.arr[root_x] = root_y\n            self.rank[root_y] += rank_x\n            \nclass Solution:\n    def findLatestStep(self, arr: List[int], m: int) -> int:\n        uf = UF(len(arr))\n        \n        sizes = {}\n        \n        seen = set()\n        last_time = None\n        for i, elt in enumerate(arr):\n            elt -= 1\n            \n            seen.add(elt)\n            left = elt - 1\n            right = elt + 1\n            if left >= 0 and left in seen and right < len(arr) and right in seen:\n                old_left_root = uf.root(left)\n                old_right_root = uf.root(right)\n\n                sizes[uf.rank[old_left_root]].remove(old_left_root)\n                if len(sizes[uf.rank[old_left_root]]) == 0:\n                    del sizes[uf.rank[old_left_root]]\n                sizes[uf.rank[old_right_root]].remove(old_right_root)\n                if len(sizes[uf.rank[old_right_root]]) == 0:\n                    del sizes[uf.rank[old_right_root]]\n                    \n                uf.union(left, elt)\n                uf.union(right, elt)\n\n            elif left >= 0 and left in seen:\n                old_left_root = uf.root(left) \n                sizes[uf.rank[old_left_root]].remove(old_left_root)\n                if len(sizes[uf.rank[old_left_root]]) == 0:\n                    del sizes[uf.rank[old_left_root]]\n                    \n                uf.union(left, elt)\n            \n            elif right < len(arr) and right in seen:\n                old_right_root = uf.root(right)\n                sizes[uf.rank[old_right_root]].remove(old_right_root)\n                if len(sizes[uf.rank[old_right_root]]) == 0:\n                    del sizes[uf.rank[old_right_root]]\n                    \n                uf.union(right, elt)\n            \n            new_root = uf.root(elt)\n            new_rank = uf.rank[new_root]\n            \n            if new_rank not in sizes:\n                sizes[new_rank] = set()\n            sizes[new_rank].add(new_root)\n\n            if m in sizes:\n                last_time = i\n            \n        if last_time is None:\n            return -1\n        else:\n            return last_time + 1\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: 9154