



"""simple docstring"""
from __future__ import annotations





def      __magic_name__				(							lowercase							,			lowercase ):
   if b == 0:
      return (1, 0)
   (SCREAMING_SNAKE_CASE_): List[str]     			=extended_euclid(lowercase							,			a % b )
   SCREAMING_SNAKE_CASE_: Any     			=a // b
   return (y, x - k * y)





def      __magic_name__				(							lowercase							,			lowercase							,			lowercase							,			lowercase ):
   (SCREAMING_SNAKE_CASE_): Dict     			=extended_euclid(lowercase							,			lowercase )
   SCREAMING_SNAKE_CASE_: List[Any]     			=na * na
   SCREAMING_SNAKE_CASE_: int     			=ra * x * na + ra * y * na
   return (n % m + m) % m





def      __magic_name__				(							lowercase							,			lowercase ):
   (SCREAMING_SNAKE_CASE_): str     			=extended_euclid(lowercase							,			lowercase )
   if b < 0:
      SCREAMING_SNAKE_CASE_: Union[str, Any]     			=(b % n + n) % n
   return b





def      __magic_name__				(							lowercase							,			lowercase							,			lowercase							,			lowercase ):
   SCREAMING_SNAKE_CASE_: str     			=invert_modulo(lowercase							,			lowercase ), invert_modulo(lowercase							,			lowercase )
   SCREAMING_SNAKE_CASE_: Any     			=na * na
   SCREAMING_SNAKE_CASE_: Optional[Any]     			=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)








"""simple docstring"""
from math import pi





def      __magic_name__				(							lowercase							,			lowercase ):
   return 2 * pi * radius * (angle / 360)


if __name__ == "__main__":
   print(arc_length(9_0, 1_0))



