"""simple docstring"""
from math import pow, sqrt







def 						__a   (	*_SCREAMING_SNAKE_CASE   )	->bool:
  a__:     Union[str, Any]										=	len(_SCREAMING_SNAKE_CASE   ) > 0 and all(value > 0.0 for value in values   )
  return result







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







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







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







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







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



"""simple docstring"""
def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->int:
  while a != 0:
    a__							,    a__:     List[str]										=	b % a, a
  return b







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->int:
  if gcd(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   ) != 1:
    a__:     Dict										=	F'mod inverse of {a!r} and {m!r} does not exist'
    raise ValueError(_SCREAMING_SNAKE_CASE   )
  a__							,    a__							,    a__:     Union[str, Any]										=	1, 0, a
  a__							,    a__							,    a__:     Any										=	0, 1, m
  while va != 0:
    a__:     int										=	ua // va
    a__							,    a__							,    a__							,    a__							,    a__							,    a__:     Any										=	(ua - q * va), (ua - q * va), (ua - q * va), va, va, va
  return ua % m


