




def        _SCREAMING_SNAKE_CASE      (		snake_case			,     snake_case       )						->				List[str]:
						if b == 0:
												return 1
						if (b % 2) == 0:
												return actual_power(snake_case			,     int(b / 2       )       ) * actual_power(snake_case			,     int(b / 2       )       )
						else:
												return a * actual_power(snake_case			,     int(b / 2       )       ) * actual_power(snake_case			,     int(b / 2       )       )




def        _SCREAMING_SNAKE_CASE      (		snake_case			,     snake_case       )						->				float:
						if b < 0:
												return 1 / actual_power(snake_case			,     snake_case       )
						return actual_power(snake_case			,     snake_case       )


if __name__ == "__main__":
				print(power(-2, -3))





from __future__ import annotations

from scipy.special import comb  # type: ignore




class       _A				:






		def __init__(    self						,		_SCREAMING_SNAKE_CASE			):
								_UpperCAmelCase      =			list_of_points
								# Degree determines the flexibility of the curve.
								# Degree = 1 will produce a straight line.
								_UpperCAmelCase      =			len(_SCREAMING_SNAKE_CASE			) - 1






		def 				UpperCAmelCase (    self						,		_SCREAMING_SNAKE_CASE			):
								assert 0 <= t <= 1, "Time t must be between 0 and 1."
								_UpperCAmelCase      =			[]
								for i in range(len(self.list_of_points			)			):
														# basis function for each i
														output_values.append(
														    comb(self.degree						,		_SCREAMING_SNAKE_CASE			) * ((1 - t) ** (self.degree - i)) * (t**i)			)
								# the basis must sum up to 1 for it to produce a valid Bezier curve.
								assert round(sum(_SCREAMING_SNAKE_CASE			)						,		5			) == 1
								return output_values






		def 				UpperCAmelCase (    self						,		_SCREAMING_SNAKE_CASE			):
								assert 0 <= t <= 1, "Time t must be between 0 and 1."

								_UpperCAmelCase      =			self.basis_function(_SCREAMING_SNAKE_CASE			)
								_UpperCAmelCase      =			0.0
								_UpperCAmelCase      =			0.0
								for i in range(len(self.list_of_points			)			):
														# For all points, sum up the product of i-th basis function and i-th point.
														x += basis_function[i] * self.list_of_points[i][0]
														y += basis_function[i] * self.list_of_points[i][1]
								return (x, y)






		def 				UpperCAmelCase (    self						,		_SCREAMING_SNAKE_CASE = 0.01			):
								from matplotlib import pyplot as plt  # type: ignore

								_UpperCAmelCase      =			[]  # x coordinates of points to plot
								_UpperCAmelCase      =			[]  # y coordinates of points to plot

								_UpperCAmelCase      =			0.0
								while t <= 1:
														_UpperCAmelCase      =			self.bezier_curve_function(_SCREAMING_SNAKE_CASE			)
														to_plot_x.append(value[0]			)
														to_plot_y.append(value[1]			)
														t += step_size

								_UpperCAmelCase      =			[i[0] for i in self.list_of_points]
								_UpperCAmelCase      =			[i[1] for i in self.list_of_points]

								plt.plot(
								    _SCREAMING_SNAKE_CASE						,		_SCREAMING_SNAKE_CASE						,		color="""blue"""						,		label="""Curve of Degree """ + str(self.degree			)						,		)
								plt.scatter(_SCREAMING_SNAKE_CASE						,		_SCREAMING_SNAKE_CASE						,		color="""red"""						,		label="""Control Points"""			)
								plt.legend()
								plt.show()


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				BezierCurve([(1, 2), (3, 5)]).plot_curve()  # degree 1
				BezierCurve([(0, 0), (5, 5), (5, 0)]).plot_curve()  # degree 2
				BezierCurve([(0, 0), (5, 5), (5, 0), (2.5, -2.5)]).plot_curve()  # degree 3