



from __future__ import annotations

from math import pi, pow
def 	UpperCamelCase			(     snake_case__ :					int | float			)			->  Optional[Any]:



			if side_length < 0:
						raise ValueError('vol_cube() only accepts non-negative values'			)
			return pow(snake_case__ ,  3			)
def 	UpperCamelCase			(     snake_case__ :					float ,  snake_case__ :					float			)			->  Any:



			if height < 0 or radius < 0:
						raise ValueError('vol_spherical_cap() only accepts non-negative values'			)
			# Volume is 1/3 pi * height squared * (3 * radius - height)
			return 1 / 3 * pi * pow(snake_case__ ,  2			) * (3 * radius - height)
def 	UpperCamelCase			(     snake_case__ :					float ,  snake_case__ :					float ,  snake_case__ :					float			)			->  List[str]:



			if radius_a < 0 or radius_a < 0 or centers_distance < 0:
						raise ValueError('vol_spheres_intersect() only accepts non-negative values'			)
			if centers_distance == 0:
						return vol_sphere(min(snake_case__ ,  snake_case__			)			)

			UpperCamelCase					:						Dict					=			(
			    (radius_a - radius_a + centers_distance)
			    * (radius_a + radius_a - centers_distance)
			    / (2 * centers_distance)
			)
			UpperCamelCase					:						Dict					=			(
			    (radius_a - radius_a + centers_distance)
			    * (radius_a + radius_a - centers_distance)
			    / (2 * centers_distance)
			)

			return vol_spherical_cap(snake_case__ ,  snake_case__			) + vol_spherical_cap(snake_case__ ,  snake_case__			)
def 	UpperCamelCase			(     snake_case__ :					float ,  snake_case__ :					float ,  snake_case__ :					float			)			->  Union[str, Any]:



			if radius_a <= 0 or radius_a <= 0 or centers_distance < 0:
						raise ValueError(
						    'vol_spheres_union() only accepts non-negative values, non-zero radius'			)

			if centers_distance == 0:
						return vol_sphere(max(snake_case__ ,  snake_case__			)			)

			return (
			    vol_sphere(snake_case__			)
			    + vol_sphere(snake_case__			)
			    - vol_spheres_intersect(snake_case__ ,  snake_case__ ,  snake_case__			)
			)
def 	UpperCamelCase			(     snake_case__ :					float ,  snake_case__ :					float ,  snake_case__ :					float			)			->  str:



			if width < 0 or height < 0 or length < 0:
						raise ValueError('vol_cuboid() only accepts non-negative values'			)
			return float(width * height * length			)
def 	UpperCamelCase			(     snake_case__ :					float ,  snake_case__ :					float			)			->  Tuple:



			if height < 0 or area_of_base < 0:
						raise ValueError('vol_cone() only accepts non-negative values'			)
			return area_of_base * height / 3.0
def 	UpperCamelCase			(     snake_case__ :					float ,  snake_case__ :					float			)			->  str:



			if height < 0 or radius < 0:
						raise ValueError('vol_right_circ_cone() only accepts non-negative values'			)
			return pi * pow(snake_case__ ,  2			) * height / 3.0
def 	UpperCamelCase			(     snake_case__ :					float ,  snake_case__ :					float			)			->  List[str]:



			if height < 0 or area_of_base < 0:
						raise ValueError('vol_prism() only accepts non-negative values'			)
			return float(area_of_base * height			)
def 	UpperCamelCase			(     snake_case__ :					float ,  snake_case__ :					float			)			->  Optional[int]:



			if height < 0 or area_of_base < 0:
						raise ValueError('vol_pyramid() only accepts non-negative values'			)
			return area_of_base * height / 3.0
def 	UpperCamelCase			(     snake_case__ :					float			)			->  Tuple:



			if radius < 0:
						raise ValueError('vol_sphere() only accepts non-negative values'			)
			# Volume is 4/3 * pi * radius cubed
			return 4 / 3 * pi * pow(snake_case__ ,  3			)
def 	UpperCamelCase			(     snake_case__ :					float			)			->  Optional[int]:



			if radius < 0:
						raise ValueError('vol_hemisphere() only accepts non-negative values'			)
			# Volume is radius cubed * pi * 2/3
			return pow(snake_case__ ,  3			) * pi * 2 / 3
def 	UpperCamelCase			(     snake_case__ :					float ,  snake_case__ :					float			)			->  Optional[Any]:



			if height < 0 or radius < 0:
						raise ValueError('vol_circular_cylinder() only accepts non-negative values'			)
			# Volume is radius squared * height * pi
			return pow(snake_case__ ,  2			) * height * pi
def 	UpperCamelCase			(     snake_case__ :					float ,  snake_case__ :					float ,  snake_case__ :					float			)			->  int:



			if inner_radius < 0 or outer_radius < 0 or height < 0:
						raise ValueError(
						    'vol_hollow_circular_cylinder() only accepts non-negative values'			)
			if outer_radius <= inner_radius:
						raise ValueError('outer_radius must be greater than inner_radius'			)
			return pi * (pow(snake_case__ ,  2			) - pow(snake_case__ ,  2			)) * height
def 	UpperCamelCase			(     snake_case__ :					float ,  snake_case__ :					float ,  snake_case__ :					float			)			->  Any:



			if radius_a < 0 or radius_a < 0 or height < 0:
						raise ValueError('vol_conical_frustum() only accepts non-negative values'			)
			return (
			    1
			    / 3
			    * pi
			    * height
			    * (pow(snake_case__ ,  2			) + pow(snake_case__ ,  2			) + radius_a * radius_a)
			)
def 	UpperCamelCase			(     snake_case__ :					float ,  snake_case__ :					float			)			->  List[str]:



			if torus_radius < 0 or tube_radius < 0:
						raise ValueError('vol_torus() only accepts non-negative values'			)
			return 2 * pow(snake_case__ ,  2			) * torus_radius * pow(snake_case__ ,  2			)
def 	UpperCamelCase			(     )			->  Optional[int]:
			print('Volumes:'			)
			print(F"""Cube: {vol_cube(2			) = }"""			)  # = 8
			print(F"""Cuboid: {vol_cuboid(2 ,  2 ,  2			) = }"""			)  # = 8
			print(F"""Cone: {vol_cone(2 ,  2			) = }"""			)  # ~= 1.33
			print(F"""Right Circular Cone: {vol_right_circ_cone(2 ,  2			) = }"""			)  # ~= 8.38
			print(F"""Prism: {vol_prism(2 ,  2			) = }"""			)  # = 4
			print(F"""Pyramid: {vol_pyramid(2 ,  2			) = }"""			)  # ~= 1.33
			print(F"""Sphere: {vol_sphere(2			) = }"""			)  # ~= 33.5
			print(F"""Hemisphere: {vol_hemisphere(2			) = }"""			)  # ~= 16.75
			print(F"""Circular Cylinder: {vol_circular_cylinder(2 ,  2			) = }"""			)  # ~= 25.1
			print(F"""Torus: {vol_torus(2 ,  2			) = }"""			)  # ~= 157.9
			print(F"""Conical Frustum: {vol_conical_frustum(2 ,  2 ,  4			) = }"""			)  # ~= 58.6
			print(F"""Spherical cap: {vol_spherical_cap(1 ,  2			) = }"""			)  # ~= 5.24
			print(F"""Spheres intersetion: {vol_spheres_intersect(2 ,  2 ,  1			) = }"""			)  # ~= 21.21
			print(F"""Spheres union: {vol_spheres_union(2 ,  2 ,  1			) = }"""			)  # ~= 45.81
			print(
			    F"""Hollow Circular Cylinder: {vol_hollow_circular_cylinder(1 ,  2 ,  3			) = }"""			)  # ~= 28.3


if __name__ == "__main__":
				main()








from __future__ import annotations

import sys
def 	UpperCamelCase			(     snake_case__ :					int ,  snake_case__ :					int			)			->  tuple[int, int]:
   # base cases
   if abs(snake_case__			) == 1:
      return a, 0
   elif abs(snake_case__			) == 1:
      return 0, b

   UpperCamelCase			,  UpperCamelCase					:						Dict					=			a, b
   UpperCamelCase			,  UpperCamelCase					:						int					=			1, 0
   UpperCamelCase			,  UpperCamelCase					:						Union[str, Any]					=			0, 1

   while remainder != 0:
      UpperCamelCase					:						str					=			old_remainder // remainder
      UpperCamelCase			,  UpperCamelCase					:						Union[str, Any]					=			remainder, old_remainder - quotient * remainder
      UpperCamelCase			,  UpperCamelCase					:						List[Any]					=			coeff_a, old_coeff_a - quotient * coeff_a
      UpperCamelCase			,  UpperCamelCase					:						Optional[Any]					=			coeff_b, old_coeff_b - quotient * coeff_b

   # sign correction for negative numbers
   if a < 0:
      UpperCamelCase					:						Dict					=			-old_coeff_a
   if b < 0:
      UpperCamelCase					:						Any					=			-old_coeff_b

   return old_coeff_a, old_coeff_b
def 	UpperCamelCase			(     )			->  Tuple:
   if len(sys.argv			) < 3:
      print('2 integer arguments required'			)
      return 1
   UpperCamelCase					:						Union[str, Any]					=			int(sys.argv[1]			)
   UpperCamelCase					:						Optional[int]					=			int(sys.argv[2]			)
   print(extended_euclidean_algorithm(snake_case__ ,  snake_case__			)			)
   return 0


if __name__ == "__main__":
    raise SystemExit(main())



