




import qiskit
from qiskit.providers import Backend




def      __magic_name__							(					A						:   int,    A						:   int  ):






			'''simple docstring'''







			a       =     bin(_snake_case  )[2:], bin(_snake_case  )[2:]  # Remove leading '0b'

			# Ensure that both strings are of the same length
			if len(_snake_case  ) > len(_snake_case  ):
						a       =     y.zfill(len(_snake_case  )  )
			else:
						a       =     x.zfill(len(_snake_case  )  )

			# We need (3 * number of bits in the larger number)+1 qBits
			# The second parameter is the number of classical registers, to measure the result
			a       =     qiskit.QuantumCircuit((len(_snake_case  ) * 3) + 1,    len(_snake_case  ) + 1  )

			# We are essentially "not-ing" the bits that are 1
			# Reversed because it's easier to perform ops on more significant bits
			for i in range(len(_snake_case  )  ):
						if x[::-1][i] == "1":
									circuit.x(_snake_case  )
			for j in range(len(_snake_case  )  ):
						if y[::-1][j] == "1":
									circuit.x(len(_snake_case  ) + j  )

			return circuit, x, y




def      __magic_name__							(					A						:   qiskit.QuantumCircuit,    A						:   int,    A						:   int,    A						:   int,    A						:   int,    ):






			'''simple docstring'''







			circuit.ccx(_snake_case,    _snake_case,    _snake_case  )
			circuit.cx(_snake_case,    _snake_case  )
			circuit.ccx(_snake_case,    _snake_case,    _snake_case  )
			circuit.cx(_snake_case,    _snake_case  )
			circuit.cx(_snake_case,    _snake_case  )




def      __magic_name__							(					A						:   int,    A						:   int,    A						:   Backend = qiskit.Aer.get_backend("aer_simulator"  ),    ):






			'''simple docstring'''







			if vala < 0 or vala < 0:
						raise ValueError("Both Integers must be positive!"  )

			# Store the Integers
			a       =     store_two_classics(_snake_case,    _snake_case  )
			for i in range(len(_snake_case  )  ):
						full_adder(_snake_case,    _snake_case,    len(_snake_case  ) + i,    len(_snake_case  ) + len(_snake_case  ) + i,    len(_snake_case  ) + len(_snake_case  ) + i + 1  )
						circuit.barrier()  # Optional, just for aesthetics

			# Measure the resultant qBits
			for i in range(len(_snake_case  ) + 1  ):
						circuit.measure([(len(_snake_case  ) * 2) + i],    [i]  )

			a       =     qiskit.execute(_snake_case,    _snake_case,    shots=1  ).result()

			# The result is in binary. Convert it back to int
			return int(list(res.get_counts()  )[0],    2  )


if __name__ == "__main__":
		import doctest

		doctest.testmod()










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

import math
import random






def 						lowercase				(	_snake_case		: int	,  _snake_case		: int	,  _snake_case		: int	)	->list[int]:
	"""simple docstring"""





	__snake_case      :		Tuple         =							d * e - 1
	__snake_case      :		List[str]         =							0
	__snake_case      :		Dict         =							0
	while p == 0:
		__snake_case      :		str         =							random.randint(2	,  n - 1	)
		__snake_case      :		int         =							k
		while True:
			if t % 2 == 0:
				__snake_case      :		int         =							t // 2
				__snake_case      :		int         =							(g**t) % n
				__snake_case      :		Optional[Any]         =							math.gcd(x - 1	,  _snake_case	)
				if x > 1 and y > 1:
					__snake_case      :		Tuple         =							y
					__snake_case      :		int         =							n // y
					break  # find the correct factors
			else:
				break  # t is not divisible by 2, break and choose another g
	return sorted([p, q]	)


if __name__ == "__main__":
			import doctest

			doctest.testmod()





