"""simple docstring"""


import itertools







def        __a (		A = 1_00_00_00   ):






     '''simple docstring'''



     lowercase__								=				[1]

     for i in itertools.count(len(A   )   ):
          lowercase__								=				0
          for j in itertools.count(1   ):
               lowercase__								=				-1 if j % 2 == 0 else +1
               lowercase__								=				(j * j * 3 - j) // 2
               if index > i:
                    break
               item += partitions[i - index] * sign
               item %= number
               index += j
               if index > i:
                    break
               item += partitions[i - index] * sign
               item %= number

          if item == 0:
               return i
          partitions.append(A   )

     return 0


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 print(F'{solution() = }')





"""simple docstring"""


import qiskit
from qiskit.providers import Backend







def        __a (		A     ,					A   ):






     '''simple docstring'''



     lowercase__			,    lowercase__								=				bin(A   )[2:], bin(A   )[2:]  # Remove leading '0b'

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

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

     return circuit, x, y







def        __a (		A     ,					A     ,					A     ,					A     ,					A     ,					):






     '''simple docstring'''



     circuit.ccx(A     ,					A     ,					A   )
     circuit.cx(A     ,					A   )
     circuit.ccx(A     ,					A     ,					A   )
     circuit.cx(A     ,					A   )
     circuit.cx(A     ,					A   )







def        __a (		A     ,					A     ,					A = qiskit.Aer.get_backend("aer_simulator"   )     ,					):






     '''simple docstring'''



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

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

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

     lowercase__								=				qiskit.execute(A     ,					A     ,					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()




