
"""simple docstring"""

def 						UpperCAmelCase   (						a_,		a_     ):





		'''simple docstring'''


		lowerCamelCase	:     str            =       1
		while b > 0:
				if b & 1:
						res *= a

				a *= a
				b >>= 1

		return res
def 						UpperCAmelCase   (						a_,		a_,		a_     ):





		'''simple docstring'''


		lowerCamelCase	:     Union[str, Any]            =       1
		while b > 0:
				if b & 1:
						lowerCamelCase	:     List[str]            =       ((res % c) * (a % c)) % c

				a *= a
				b >>= 1

		return res








"""simple docstring"""

def 						UpperCAmelCase   (						a_     ):





		'''simple docstring'''


		if not isinstance(a_,		a_     ):
				raise TypeError('recursive_lucas_number accepts only integer arguments.'     )
		if n_th_number == 0:
				return 2
		if n_th_number == 1:
				return 1

		return recursive_lucas_number(n_th_number - 1     ) + recursive_lucas_number(
		    n_th_number - 2     )
def 						UpperCAmelCase   (						a_     ):





		'''simple docstring'''


		if not isinstance(a_,		a_     ):
				raise TypeError('dynamic_lucas_number accepts only integer arguments.'     )
		lowerCamelCase      ,       lowerCamelCase	:     Optional[int]            =       2, 1
		for _ in range(a_     ):
				lowerCamelCase      ,       lowerCamelCase	:     Optional[int]            =       b, a + b
		return a


if __name__ == "__main__":
					from doctest import testmod

					testmod()
					_A				=					int(input('Enter the number of terms in lucas series:\n').strip())
					print('Using recursive function to calculate lucas series:')
					print(' '.join(str(recursive_lucas_number(i)) for i in range(n)))
					print('\nUsing dynamic function to calculate lucas series:')
					print(' '.join(str(dynamic_lucas_number(i)) for i in range(n)))






