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#         #两个数组，一个记录长度，另一个记录长度的个数\n#         length = [0 for _ in range(len(arr)+2)]\n#         count = [0 for _ in range(len(arr)+1)]\n#         res = -1\n#         for i, a in enumerate(arr):\n#             #先把左边的长度和右边的1长度取出来\n#             left, right = length[a-1], length[a+1]\n#             #现在这个位置的长度就是左边的长度加上右边的长度加上自己\n#             #距离a位置的左右两边的边角处的索引也会被附上新的值，之后的计算可能用得上\n#             length[a] = length[a-left] = length[a+right] = left + right + 1\n            \n#             #然后就是更新count了\n#             count[left] -= 1\n#             count[right] -= 1\n#             count[length[a]] += 1\n            \n#             #判断m是否还存在，只要m存在那就是满足条件的最后一步\n#             if count[m]:\n#                 res = i+1\n#         return res\n\nclass UnionFindSet:\n    def __init__(self, n):\n        self.parents = [i for i in range(n)]\n        self.ranks = [0 for _ in range(n)] #表示index位置的1的长度\n\n    def find(self, u):\n        if u != self.parents[u]:\n            self.parents[u] = self.find(self.parents[u])\n        return self.parents[u]\n    \n    def union(self, u, v):\n        pu, pv = self.find(u), self.find(v)\n        if pu == pv:\n            return False\n        \n        #作为父亲节点的条件，谁的长度比较大。就跟着谁。 如果长度相同时会不会有问题? 感觉这里写得不对，长度相同时应该看pu和pv哪个比较大(小). 也许按长度来作为父亲节点并没有影响，也可以尝试找索引值较小的元素作为父亲节点\n        # if self.ranks[pu] > self.ranks[pv]:\n        #     self.parents[pv] = self.parents[pu]\n        #     self.ranks[pu] += self.ranks[pv] #这里只修改pu的1长度原因是，以后查询pv的长度都会指向pu的长度\n        # else:\n        #     self.parents[pu] = self.parents[pv]\n        #     self.ranks[pv] += self.ranks[pu]\n        self.parents[max(pu,pv)] = min(pu, pv)\n        self.ranks[min(pu,pv)] += self.ranks[max(pu,pv)]\n             \n        return True\nclass Solution:\n    def findLatestStep(self, arr: List[int], m: int) -> int:\n        if len(arr) == m: #最后一步\n            return m\n        \n        uf = UnionFindSet(len(arr))\n        n, ans = len(arr), -1\n        \n        for step, a in enumerate(arr):\n            a -= 1 #字符串索引从0开始\n            \n            uf.ranks[a] = 1\n            #找左右节点进行联结\n            for j in (a-1, a+1):\n                if 0 <= j < n:\n                    if uf.ranks[uf.find(j)] == m:\n                        #上一步还存在m长度的1群. 也许在其他地方还有存在m长度的，但是后面会遍历到. 注意这里遍历不到最后一步\n                        ans = step\n                    #如果j位置上是1,即1的群长度大于0。 则可以进行连接\n                    if uf.ranks[j] > 0:\n                        uf.union(a , j)\n                        \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

```

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