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        n = len(arr)\n        que = collections.deque([(1, n)])\n        \n        for i in range(n-1, -1, -1):\n            \n            k = len(que)\n            \n            for j in range(k):\n                l, r = que.popleft()\n                if r - l + 1 == m:\n                    return i+1\n                \n                if l <= arr[i] <= r:\n                    if arr[i]-l >= m:\n                        que.append((l, arr[i]-1))\n                    if r-arr[i] >= m:\n                        que.append((arr[i]+1, r))\n                else:\n                    que.append((l, r))\n        return -1\n            \n            \n            \n        \n        \n        \n        # change endpoint .\n        # n = len(arr)\n        # if m == n:\n        #     return m\n        # length = [0] * (n+2)\n        # # count = [0] * (n+1)\n        # res = -1\n        # for i, num in enumerate(arr):\n        #     left = length[num-1]\n        #     right = length[num + 1]\n        #     # I almost came up with this, change the endpoint.\n        #     length[num-left] = length[num+right] = left+right+1\n        #     if left == m or right == m:\n        #         res = i\n        # return res\n    \n    \n    \n    # if m == len(A): return m\n    #     length = [0] * (len(A) + 2)\n    #     res = -1\n    #     for i, a in enumerate(A):\n    #         left, right = length[a - 1], length[a + 1]\n    #         if left == m or right == m:\n    #             res = i\n    #         length[a - left] = length[a + right] = left + right + 1\n    #     return res\n                \n            \n            \n                \n            \n            \n        # Union-find\n#         n = len(arr)\n#         p = [i for i in range(n+1)]\n#         count = [0] * (n+1)\n#         ### I didn't come up with this groups at first. It shouldn't be hard.\n#         groups = [0] * (n+1)\n#         def findp(x):\n#             while x != p[x]:\n#                 x = p[x]\n#             return x\n        \n#         def union(x, y):\n            \n#             groups[count[y]] -= 1\n#             groups[count[x]] -= 1\n#             if count[x] >= count[y]:\n#                 p[y] = x\n#                 count[x] += count[y]\n#                 groups[count[x]] += 1\n#             else:\n#                 p[x] = y\n#                 count[y] += count[x]\n#                 groups[count[y]] += 1\n        \n#         res = -1\n        \n#         for i, num in enumerate(arr):\n#             # print(p)\n#             # print(count)\n#             count[num] = 1\n#             left = num-1\n#             right = num + 1\n#             groups[1] += 1\n#             if left >= 1 and count[left] != 0:\n#                 pl = findp(left)\n#                 pm = findp(num)\n#                 if pl != pm:\n#                     union(pl, pm)\n#             if right <= n and count[right] != 0:\n#                 pr = findp(right)\n#                 pm = findp(num)\n#                 if pr != pm:\n#                     union(pr, pm)\n            \n#             if groups[m] > 0:\n#                 res = i+1\n#         return res\n                    \n                \n                \n            \n        \n                \n        \n        \n        \n        \n         \n        \n            \n            \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

```

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