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    \n    def __init__(self, n):\n        self.parent = list(range(n))\n        self.rank = [0]*n\n        self.size = [0]*n\n        self.groupCount = [0]*(n+1)\n    \n    def find(self, x):\n        if x != self.parent[x]:\n            self.parent[x] = self.find(self.parent[x])\n        return self.parent[x]\n    \n    def add(self, x):\n        self.size[x] = 1\n        self.groupCount[1] += 1\n    \n    def union(self, x, y):\n        px = self.find(x)\n        py = self.find(y)\n        if px == py:\n            return False\n        if self.groupCount[self.size[px]] > 0: \n            self.groupCount[self.size[px]] -= 1\n        if self.groupCount[self.size[py]] > 0:\n            self.groupCount[self.size[py]] -= 1\n        if self.rank[px] > self.rank[py]:\n            self.parent[py] = px\n            self.size[px] += self.size[py]\n            self.size[py] = 0\n        elif self.rank[py] > self.rank[px]:\n            self.parent[px] = py\n            self.size[py] += self.size[px]\n            self.size[px] = 0\n        else:\n            self.parent[px] = py\n            self.size[py] += self.size[px]\n            self.size[px] = 0\n            self.rank[py] += 1\n        self.groupCount[self.size[px]] += 1\n        self.groupCount[self.size[py]] += 1\n        return True\n    \n    def getSize(self, i):\n        px = self.find(i)\n        return self.size[px]\n    \nclass Solution:\n    \n    def findLatestStep(self, arr: List[int], m: int) -> int:\n        disjoint = UnionFind(len(arr))\n        ans = - 1\n        val = [0]*len(arr)\n        for k in range(len(arr)):\n            index = arr[k] - 1\n            val[index] += 1\n            disjoint.add(index)\n            if index > 0 and val[index] == val[index-1]:\n                disjoint.union(index, index - 1)\n            if index + 1 < len(val) and val[index] == val[index+1]:\n                disjoint.union(index, index + 1)\n            #print(k, disjoint.groupCount)\n            if disjoint.groupCount[m] > 0:\n                ans = k + 1\n            '''\n            i = 0\n            while i < len(arr):\n                if val[i] == 1 and disjoint.getSize(i) == m:\n                    i += disjoint.getSize(i)\n                    ans = k + 1\n                    continue\n                i += 1\n            '''\n            #print(k, disjoint.size, val)\n        return ans \n    \n    '''\n    def findLatestStep(self, arr: List[int], m: int) -> int:\n        def check(i):\n            val = [0]*len(arr)\n            for k in range(i+1):\n                val[arr[k]-1] = 1\n            count = 0\n            success = False\n            for k in range(len(val)):\n                if val[k] > 0:\n                    count += 1\n                else:\n                    if count == m:\n                        success = True\n                        break\n                    count = 0\n            if count == m:\n                success = True\n            return success                \n            \n        left = 0\n        right = len(arr)\n        while left < right:\n            mid = left + (right - left) //2\n            if not check(mid):\n                right = mid\n            else:\n                left = mid + 1\n        print(left)\n        if left == 0 and not check(left):\n            return -1\n        else:\n            return left\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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