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#         arr = arr[::-1]\n#         s = \\"1\\"*len(arr)\n#         step = len(arr)\n#         for j in arr:\n#             group = s.split(\\"0\\")\n#             group = list(set(group))\n#             if \\"1\\"*m in group:\n#                 return step\n#             step -=1\n#             s = s[:j-1] + \\"0\\" + s[j:]\n#         return -1\n            \n            \nclass UF:\n    def __init__(self, n, m):\n        self.p = [i for i in range(n+1)]  # parent for each position\n        self.c = [0 for _ in range(n+1)]  # length of group for each position\n        self.m_cnt = 0                    # count of group with length m\n        self.m = m                        # m\n        \n    def union(self, i, j):\n        pi, pj = self.find(i), self.find(j)\n        if pi != pj:\n            if self.c[pi] == self.m: self.m_cnt -= 1  # if previous length at pi is m, decrement m_cnt by 1\n            if self.c[pj] == self.m: self.m_cnt -= 1  # if previous length at pj is m, decrement m_cnt by 1\n            self.p[pj] = pi                           # union, use pi at parent for pj\n            self.c[pi] += self.c[pj]                  # update new length at pi\n            if self.c[pi] == self.m: self.m_cnt += 1  # if new length at pi == m, increment m_cnt by 1\n            \n    def mark(self, i):                                \n        self.c[i] = 1                                 # when first visit a point, mark length as 1\n        if self.m == 1: self.m_cnt += 1               # if self.m == 1, increment m_cnt by 1\n        \n    def find(self, i):                                # find parent of i\n        if self.p[i] != i:\n            self.p[i] = self.find(self.p[i])\n        return self.p[i]\n    \nclass Solution:\n    def findLatestStep(self, arr: List[int], m: int) -> int:\n        n = len(arr)\n        uf, ans = UF(n, m), -1                                   # create union find and answer\n        for i, num in enumerate(arr, 1):\n            uf.mark(num)\n            if num-1 >= 1 and uf.c[num-1]: uf.union(num-1, num)  # if left neighbor is marked, union the two\n            if num+1 < n+1 and uf.c[num+1]: uf.union(num+1, num) # if right neighbor is marked, union the two\n                \n            if uf.m_cnt > 0: ans = i                             # if m_cnt > 0, meaning there exists some group with length m, update ans\n        return ans'
_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: 7228