Recently Kazakov, Vieira and the author conjectured the Y system set of equations describing the planar spectrum of AdS/CFT. In this paper we solve the Y system equations in the strong coupling scaling limit. We show that the quasiclassical spectrum of string moving inside AdS3 x S1 matches precisely with the prediction of the Y system. Thus the Y system, unlike the asymptotic Bethe ansatz, describes correctly the spectrum of one-loop string energies including all exponential finite size corrections. This gives a very non-trivial further support in favor of the conjecture. We also discuss how the generalization to the full AdS5 x S5 can be easily constructed using the PSU(2,2 4) symmetry of the problem.