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 UnionFind:\n#     def __init__(self, n):\n#         self.parent = {}\n#         self.rank = [0] * (n+1)\n#         self.group_size = defaultdict(list)\n    \n#     def find(self, x):\n#         if x not in self.parent:\n#             self.parent[x] = x\n#             self.rank[x] = 1\n#             self.group_size[1].append(x)\n\nclass UnionFind:\n        def __init__(self, m, n):\n            self.m = m\n            self.parents = [i for i in range(n+1)]\n            # self.ranks = [1 for _ in range(n)]\n            self.group_size = defaultdict(set)\n            # self.group_size[1] = set([i+1 for i in range(n)])\n            self.sizes = defaultdict(int)\n            # for i in range(n):\n            #     self.sizes[i+1] = 1\n\n        def find(self, x):\n            if self.parents[x]!=x:\n                self.parents[x] = self.find(self.parents[x])\n            return self.parents[x]\n\n        def union(self, x, y):\n            root_x, root_y = self.find(x), self.find(y)\n            # print(\\"x\\", x ,\\"y\\", y)\n            # print(\\"root_x\\", root_x ,\\"root_y\\", root_y)\n            self.parents[root_x] = root_y\n            size_root_x = self.sizes[root_x]\n            self.sizes[root_x] = 0\n            self.group_size[size_root_x].remove(root_x)\n\n            size_root_y = self.sizes[root_y]\n            self.group_size[size_root_y].remove(root_y)\n            self.sizes[root_y] = size_root_y + size_root_x\n            self.group_size[self.sizes[root_y]].add(root_y)\n            \n            \n            # print(\\"len(self.group_size[self.m])\\", len(self.group_size[self.m]))\n            if len(self.group_size[self.m])>0:\n                return True\n            else:\n                return False\n            \n\nclass Solution:\n    ## my own solution: union find\n    ## mapping between sizes and positions\n    def findLatestStep(self, arr: List[int], m: int) -> int:\n        n = len(arr)\n        uf = UnionFind(m, n)\n        # print(uf.group_size)\n        # print(uf.sizes)\n        seen = set()\n        res = -1\n        for idx, x in enumerate(arr):\n            seen.add(x)\n            uf.sizes[x] = 1\n            uf.group_size[1].add(x)\n            if x-1 in seen:\n                uf.union(x, x-1)\n                # if len(uf.group_size[m])>0:\n                #     res = idx+1\n            if x+1 in seen:        \n                uf.union(x+1, x)\n                \n            if len(uf.group_size[m])>0:\n                res = idx+1\n            # print(\\"uf.group_size\\", uf.group_size)\n            # print(\\"uf.sizes\\", uf.sizes)\n        return res\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: 9512