Given a binary string S (a string consisting only of '0' and '1's) and a positive integer N, return true if and only if for every integer X from 1 to N, the binary representation of X is a substring of S.
 
Example 1:
Input: S = "0110", N = 3
Output: true

Example 2:
Input: S = "0110", N = 4
Output: false

 
Note:

1 <= S.length <= 1000
1 <= N <= 10^9

```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 = '\nclass Solution:\n    def queryString(self, S: str, N: int) -> bool:\n        n = len(S)\n        for i in range(30,-1,-1):\n            if N&(1<<i):\n                msb = i\n                break\n        def get(msb):\n            s =  set()\n            num = 0\n            x = 0\n            if msb > 0:\n                x = 1<<(msb-1)\n            for i in range(n):\n                if i == msb:\n                    if S[i] == \'1\':\n                        num += 1\n                    if x < num <= N:\n                        s.add(num)\n                elif(i > msb):\n                    # print(num,end=\\" \\")\n                    if num&(1<<msb):\n                        num -= (1<<msb)\n                    num <<= 1\n                    if S[i] == \'1\':\n                        num += 1\n                    if x < num <= N:\n                        s.add(num)\n                else:\n                    if S[i]==\'1\':\n                        num |= (1<<(msb- i))\n            return s\n        \n        s = get(msb)\n        p = 0\n        if msb > 0:\n            p = 1<<(msb-1)\n        if msb > 0:\n            s1 = get(msb-1)\n            p = 0\n            if msb > 1:\n                p = 1<<(msb-2)\n            for i in s1:\n                s.add(i)\n        # print(list(s),p)\n        return len(s) == (N - p)\n        \n         \n    \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'queryString'
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: 6590