






"""simple docstring"""





def      lowerCamelCase__       (							_lowerCamelCase       :		int		,				_lowerCamelCase       :		int )      ->				str:
  if a < 0 or b < 0:
    raise ValueError('the value of both inputs must be positive' )
  lowerCamelCase_         =						str(bin(_lowerCamelCase ) )[2:]  # remove the leading "0b"
  lowerCamelCase_         =						str(bin(_lowerCamelCase ) )[2:]
  lowerCamelCase_         =						max(len(_lowerCamelCase )		,				len(_lowerCamelCase ) )
  return "0b" + "".join(
      str(int('1' in (char_a, char_b) ) )
      for char_a, char_b in zip(a_binary.zfill(_lowerCamelCase )		,				b_binary.zfill(_lowerCamelCase ) ) )


if __name__ == "__main__":
  import doctest

  doctest.testmod()












"""simple docstring"""





from math import pow, sqrt







def      lowerCamelCase__       (							*_lowerCamelCase       :		float )      ->				bool:
  lowerCamelCase_         =						len(_lowerCamelCase ) > 0 and all(value > 0.0 for value in values )
  return result







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(sqrt(molar_mass_a / molar_mass_a )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase )
      else ValueError('Input Error: Molar mass values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(effusion_rate * sqrt(molar_mass_a / molar_mass_a )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(effusion_rate / sqrt(molar_mass_a / molar_mass_a )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(molar_mass / pow(effusion_rate_a / effusion_rate_a		,				2 )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(pow(effusion_rate_a / effusion_rate_a		,				2 ) / molar_mass		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )




