





"""simple docstring"""
def      __lowerCamelCase   (							a_     :		int ,   a_     :		str							)			->      Optional[int]:
      __SCREAMING_SNAKE_CASE   :Optional[int]						=  [1]
      for i in range(2 ,   a_							):
            factorials.append(factorials[-1] * i							)
      assert 0 <= k < factorials[-1] * n, "k out of bounds"

      __SCREAMING_SNAKE_CASE   :List[str]						=  []
      __SCREAMING_SNAKE_CASE   :Optional[Any]						=  list(range(a_							)							)

      # Find permutation
      while factorials:
            __SCREAMING_SNAKE_CASE   :Optional[int]						=  factorials.pop()
            __SCREAMING_SNAKE_CASE				,__SCREAMING_SNAKE_CASE   :Dict						=  divmod(a_ ,   a_							)
            permutation.append(elements[number]							)
            elements.remove(elements[number]							)
      permutation.append(elements[0]							)

      return permutation


if __name__ == "__main__":
  import doctest

  doctest.testmod()






"""simple docstring"""
import qiskit



def      __lowerCamelCase   (							a_     :		int ,   a_     :		int							)			->      qiskit.result.counts.Counts:
      __SCREAMING_SNAKE_CASE   :Tuple						=  qiskit.Aer.get_backend('''aer_simulator'''							)

      # Create a Quantum Circuit acting on the q register
      __SCREAMING_SNAKE_CASE   :Union[str, Any]						=  qiskit.QuantumCircuit(a_ ,   a_							)

      # Apply X (NOT) Gate to Qubits 0 & 1
      circuit.x(0							)
      circuit.x(1							)

      # Map the quantum measurement to the classical bits
      circuit.measure([0, 1] ,   [0, 1]							)

      # Execute the circuit on the qasm simulator
      __SCREAMING_SNAKE_CASE   :Tuple						=  qiskit.execute(a_ ,   a_ ,   shots=10_00							)

      # Return the histogram data of the results of the experiment.
      return job.result().get_counts(a_							)


if __name__ == "__main__":
  lowerCamelCase_								=		single_qubit_measure(2, 2)
  print(f'Total count for various states are: {counts}')