




"""simple docstring"""

def 		_snake_case	(   _snake_case				:   int							,    _snake_case				:   int				)       ->   int:






      '''simple docstring'''


      while a != 0:
            _A  ,       _A     =  b % a, a
      return b







def 		_snake_case	(   _snake_case				:   int							,    _snake_case				:   int				)       ->   int:






      '''simple docstring'''


      if gcd(_snake_case							,    _snake_case				) != 1:
            _A     =  F'''mod inverse of {a!r} and {m!r} does not exist'''
            raise ValueError(_snake_case				)
      _A  ,       _A  ,       _A     =  1, 0, a
      _A  ,       _A  ,       _A     =  0, 1, m
      while va != 0:
            _A     =  ua // va
            _A  ,       _A  ,       _A  ,       _A  ,       _A  ,       _A     =  (ua - q * va), (ua - q * va), (ua - q * va), va, va, va
      return ua % m







"""simple docstring"""

import math






def 		_snake_case	(   _snake_case				:   float							,    _snake_case				:   float				)       ->   float:






      '''simple docstring'''


      if (
          not isinstance(_snake_case							,    (int, float)				)
          or power_factor < -1
          or power_factor > 1
      ):
            raise ValueError('power_factor must be a valid float value between -1 and 1.'				)
      return apparent_power * power_factor






def 		_snake_case	(   _snake_case				:   float							,    _snake_case				:   float				)       ->   float:






      '''simple docstring'''


      if (
          not isinstance(_snake_case							,    (int, float)				)
          or power_factor < -1
          or power_factor > 1
      ):
            raise ValueError('power_factor must be a valid float value between -1 and 1.'				)
      return apparent_power * math.sqrt(1 - power_factor**2				)


if __name__ == "__main__":
       import doctest

       doctest.testmod()

