


'''simple docstring'''
def 	_A  (       A							,A							)  ->				str:
	if number < 0 or shift_amount < 0:
		raise ValueError("both inputs must be positive integers"							)

	lowercase						:		Tuple   					=		str(bin(A							)							)
	binary_number += "0" * shift_amount
	return binary_number




def 	_A  (       A							,A							)  ->				str:
	if number < 0 or shift_amount < 0:
		raise ValueError("both inputs must be positive integers"							)

	lowercase						:		Union[str, Any]   					=		str(bin(A							)							)[2:]
	if shift_amount >= len(A							):
		return "0b0"
	lowercase						:		Optional[Any]   					=		binary_number[: len(A							) - shift_amount]
	return "0b" + shifted_binary_number




def 	_A  (       A							,A							)  ->				str:
	if number >= 0:  # Get binary representation of positive number
		lowercase						:		List[str]   					=		"0" + str(bin(A							)							).strip("-"							)[2:]
	else:  # Get binary (2's complement) representation of negative number
		lowercase						:		Tuple   					=		len(bin(A							)[3:]							)  # Find 2's complement of number
		lowercase						:		List[str]   					=		bin(abs(A							) - (1 << binary_number_length)							)[3:]
		lowercase						:		int   					=		(
		    "1" + "0" * (binary_number_length - len(A							)) + binary_number
		)

	if shift_amount >= len(A							):
		return "0b" + binary_number[0] * len(A							)
	return (
	    "0b"
	    + binary_number[0] * shift_amount
	    + binary_number[: len(A							) - shift_amount]
	)


if __name__ == "__main__":
					import doctest

					doctest.testmod()






'''simple docstring'''
def 	_A  (       A							)  ->				list:
	lowercase						:		str   					=		int(A							)
	if n_element < 1:
		lowercase						:		List[Any]   					=		ValueError("a should be a positive number"							)
		raise my_error

	lowercase						:		List[Any]   					=		[1]
	lowercase					,		lowercase					,		lowercase						:		Tuple   					=		(0, 0, 0)
	lowercase						:		Dict   					=		1
	while index < n_element:
		while hamming_list[i] * 2 <= hamming_list[-1]:
			i += 1
		while hamming_list[j] * 3 <= hamming_list[-1]:
			j += 1
		while hamming_list[k] * 5 <= hamming_list[-1]:
			k += 1
		hamming_list.append(
		    min(hamming_list[i] * 2							,hamming_list[j] * 3							,hamming_list[k] * 5							)							)
		index += 1
	return hamming_list


if __name__ == "__main__":
					lowerCAmelCase   : Union[str, Any]             =				input("""Enter the last number (nth term) of the Hamming Number Series: """)
					print("""Formula of Hamming Number Series => 2^i * 3^j * 5^k""")
					lowerCAmelCase   : Tuple             =				hamming(int(n))
					print("""-----------------------------------------------------""")
					print(F'''The list with nth numbers is: {hamming_numbers}''')
					print("""-----------------------------------------------------""")


