


'''simple docstring'''

from math import pow, sqrt





def __snake_case      (   *UpperCAmelCase_		:		float	):
 lowerCamelCase_  				=						len(UpperCAmelCase_	) > 0 and all(value > 0.0 for value in values	)
 return result





def __snake_case      (   UpperCAmelCase_		:		float      ,       UpperCAmelCase_		:		float	):
 return (
     round(sqrt(molar_mass_a / molar_mass_a	)      ,       6	)
     if validate(UpperCAmelCase_      ,       UpperCAmelCase_	)
     else ValueError("Input Error: Molar mass values must greater than 0."	)
 )





def __snake_case      (   UpperCAmelCase_		:		float      ,       UpperCAmelCase_		:		float      ,       UpperCAmelCase_		:		float	):
 return (
     round(effusion_rate * sqrt(molar_mass_a / molar_mass_a	)      ,       6	)
     if validate(UpperCAmelCase_      ,       UpperCAmelCase_      ,       UpperCAmelCase_	)
     else ValueError(
         "Input Error: Molar mass and effusion rate values must greater than 0."	)
 )





def __snake_case      (   UpperCAmelCase_		:		float      ,       UpperCAmelCase_		:		float      ,       UpperCAmelCase_		:		float	):
 return (
     round(effusion_rate / sqrt(molar_mass_a / molar_mass_a	)      ,       6	)
     if validate(UpperCAmelCase_      ,       UpperCAmelCase_      ,       UpperCAmelCase_	)
     else ValueError(
         "Input Error: Molar mass and effusion rate values must greater than 0."	)
 )





def __snake_case      (   UpperCAmelCase_		:		float      ,       UpperCAmelCase_		:		float      ,       UpperCAmelCase_		:		float	):
 return (
     round(molar_mass / pow(effusion_rate_a / effusion_rate_a      ,       2	)      ,       6	)
     if validate(UpperCAmelCase_      ,       UpperCAmelCase_      ,       UpperCAmelCase_	)
     else ValueError(
         "Input Error: Molar mass and effusion rate values must greater than 0."	)
 )







def __snake_case      (   UpperCAmelCase_		:		float      ,       UpperCAmelCase_		:		float      ,       UpperCAmelCase_		:		float	):
 return (
     round(pow(effusion_rate_a / effusion_rate_a      ,       2	) / molar_mass      ,       6	)
     if validate(UpperCAmelCase_      ,       UpperCAmelCase_      ,       UpperCAmelCase_	)
     else ValueError(
         "Input Error: Molar mass and effusion rate values must greater than 0."	)
 )







'''simple docstring'''

from __future__ import annotations





def __snake_case      (   UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int	):
 if b == 0:
  return (1, 0)
 ((lowerCamelCase_)				,(lowerCamelCase_))  				=						extended_euclid(UpperCAmelCase_      ,       a % b	)
 lowerCamelCase_  				=						a // b
 return (y, x - k * y)





def __snake_case      (   UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int	):
 ((lowerCamelCase_)				,(lowerCamelCase_))  				=						extended_euclid(UpperCAmelCase_      ,       UpperCAmelCase_	)
 lowerCamelCase_  				=						na * na
 lowerCamelCase_  				=						ra * x * na + ra * y * na
 return (n % m + m) % m





def __snake_case      (   UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int	):
 ((lowerCamelCase_)				,(lowerCamelCase_))  				=						extended_euclid(UpperCAmelCase_      ,       UpperCAmelCase_	)
 if b < 0:
  lowerCamelCase_  				=						(b % n + n) % n
 return b





def __snake_case      (   UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int	):
 lowerCamelCase_				,lowerCamelCase_  				=						invert_modulo(UpperCAmelCase_      ,       UpperCAmelCase_	), invert_modulo(UpperCAmelCase_      ,       UpperCAmelCase_	)
 lowerCamelCase_  				=						na * na
 lowerCamelCase_  				=						ra * x * na + ra * y * na
 return (n % m + m) % m


if __name__ == "__main__":
     from doctest import testmod

     testmod(name="""chinese_remainder_theorem""", verbose=True)
     testmod(name="""chinese_remainder_theorem2""", verbose=True)
     testmod(name="""invert_modulo""", verbose=True)
     testmod(name="""extended_euclid""", verbose=True)



