Given a positive integer K, you need find the smallest positive integer N such that N is divisible by K, and N only contains the digit 1.
Return the length of N.  If there is no such N, return -1.
 
Example 1:
Input: 1
Output: 1
Explanation: The smallest answer is N = 1, which has length 1.
Example 2:
Input: 2
Output: -1
Explanation: There is no such positive integer N divisible by 2.
Example 3:
Input: 3
Output: 3
Explanation: The smallest answer is N = 111, which has length 3.
 
Note:

1 <= K <= 10^5

```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 smallestRepunitDivByK(self, K: int) -> int:\n    # Say k = 3:\n    # 1 mod 3 = 1\n    # 10 mod 3 = 1\n    # 100 mod 3 = 1\n    # and we are done because each of the components contributes 1 to the modulo, and 3 of them completes it.\n    \n    # 1 mod 2 = 1\n    # 10 mod 2 = 0\n    # 100 mod 2 = 0\n    # and all subsequent powers of 10 all contribute 0, so it's impossible.\n    \n    # Obviously all even K is impossible, because even * anything = even and 11...11 is always odd.\n    \n    # Is any odd K always possible? No. Clearly ***5 is not possible. \n    # 1 mod 5 = 1\n    # 10 mod 5 = 0\n    # 100 mod 5 = 0\n    # and so forth.\n    \n    # 1 mod 15 = 1\n    # 10 mod 15 = 10\n    # 100 mod 15 = 10\n    # 1000 mod 15 = 10\n    # and so forth.\n    \n    # Once a duplicate happens, why will it keep happening?\n    # Say  1...1 (d digits) % K = m\n    # Then 1....1 (d+1 digits) % K = (1...1 x 10 + 1) % K = (m x 10 + 1) % K\n    # Thus the next mod is determined by the previous mod. \n    if K % 10 not in [1, 3, 7, 9]: return -1\n    m = 0\n    for d in range(1, K + 1):\n        m = (m * 10 + 1) % K\n        if not m: return d\n    return -1"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'smallestRepunitDivByK'
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: 5366