class BitWriter:
  def __init__(self) -> None:
    self._bits: list[int] = []

  @property
  def bit_length(self) -> int:
    return len(self._bits)

  def write(self, value: int, width: int) -> None:
    if width < 0:
      raise ValueError("width must be positive")
    if value < 0 or value >= (1 << width):
      raise ValueError(f"value {value} does not fit in {width} bits")
    for shift in range(width - 1, -1, -1):
      self._bits.append((value >> shift) & 1)

  def to_bytes(self) -> bytes:
    padding = (-len(self._bits)) % 8
    bits = self._bits + [0] * padding
    out = bytearray()
    for i in range(0, len(bits), 8):
      byte = 0
      for bit in bits[i : i + 8]:
        byte = (byte << 1) | bit
      out.append(byte)
    return bytes(out)

class BitReader:
  def __init__(self, data: bytes, bit_length: int) -> None:
    self._bits: list[int] = []
    for byte in data:
      for shift in range(7, -1, -1):
        self._bits.append((byte >> shift) & 1)
    self._bits = self._bits[:bit_length]
    self._pos = 0

  def read(self, width: int) -> int:
    if self._pos + width > len(self._bits):
      raise ValueError("payload ended unexpectedly")
    value = 0
    for bit in self._bits[self._pos : self._pos + width]:
      value = (value << 1) | bit
    self._pos += width
    return value

  @property
  def remaining(self) -> int:
    return len(self._bits) - self._pos