  We show that any stochastic differential equation (SDE) driven by Brownian
motion with drift satisfying the Krylov-R\"ockner condition has exactly one
solution in an ordinary sense for almost every trajectory of the Brownian
motion. Additionally, we show that such SDE is strongly complete, i.e. for
almost every trajectory of the Brownian motion, the family of solutions with
different initial data forms a continuous semiflow for all nonnegative times.
