
import qiskit
from qiskit.providers import Backend


def  A__ (       __lowerCamelCase,  __lowerCamelCase						):
   SCREAMING_SNAKE_CASE_	=      bin(__UpperCAmelCase						)[2:], bin(__UpperCAmelCase						)[2:]  # Remove leading '0b'

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

   # 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
   SCREAMING_SNAKE_CASE_	=      qiskit.QuantumCircuit((len(__UpperCAmelCase						) * 3) + 1,  len(__UpperCAmelCase						) + 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(__UpperCAmelCase						)						):
      if x[::-1][i] == "1":
         circuit.x(__UpperCAmelCase						)
   for j in range(len(__UpperCAmelCase						)						):
      if y[::-1][j] == "1":
         circuit.x(len(__UpperCAmelCase						) + j						)

   return circuit, x, y


def  A__ (       __lowerCamelCase,  __lowerCamelCase,  __lowerCamelCase,  __lowerCamelCase,  __lowerCamelCase,  ):
   circuit.ccx(__UpperCAmelCase,  __UpperCAmelCase,  __UpperCAmelCase						)
   circuit.cx(__UpperCAmelCase,  __UpperCAmelCase						)
   circuit.ccx(__UpperCAmelCase,  __UpperCAmelCase,  __UpperCAmelCase						)
   circuit.cx(__UpperCAmelCase,  __UpperCAmelCase						)
   circuit.cx(__UpperCAmelCase,  __UpperCAmelCase						)


def  A__ (       __lowerCamelCase,  __lowerCamelCase,  __lowerCamelCase = qiskit.Aer.get_backend('''aer_simulator'''						),  ):





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

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

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

   SCREAMING_SNAKE_CASE_	=      qiskit.execute(__UpperCAmelCase,  __UpperCAmelCase,  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   __lowerCAmelCase(		__UpperCAmelCase  ,__UpperCAmelCase  ,__UpperCAmelCase      ):






	"""simple docstring"""





	_lowercase			:     Optional[int]      					=				d * e - 1
	_lowercase			:     int      					=				0
	_lowercase			:     Union[str, Any]      					=				0
	while p == 0:
		_lowercase			:     int      					=				random.randint(2  ,n - 1      )
		_lowercase			:     str      					=				k
		while True:
			if t % 2 == 0:
				_lowercase			:     List[Any]      					=				t // 2
				_lowercase			:     int      					=				(g**t) % n
				_lowercase			:     Tuple      					=				math.gcd(x - 1  ,__UpperCAmelCase      )
				if x > 1 and y > 1:
					_lowercase			:     List[str]      					=				y
					_lowercase			:     str      					=				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()



