




def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> int:
       while a != 0:
              lowerCamelCase ,      lowerCamelCase   :      Optional[int]			 =					b % a, a
       return b


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












import math

def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> float:
       if (
           not isinstance(_SCREAMING_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      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> float:
       if (
           not isinstance(_SCREAMING_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()






