  The Statistical Model of the Early Stage, SMES, describes a transition
between confined and deconfined phases of strongly interacting matter created
in nucleus-nucleus collisions. The model was formulated in the late 1990s for
central Pb+Pb collisions at the CERN SPS energies. It predicted several signals
of the transition (onset of deconfinement) which were later observed by the
NA49 experiment. The grand canonical ensemble was used to calculate entropy and
strangeness production. This approximation is valid for reactions with mean
multiplicities of particles carrying conserved charges being significantly
larger than one.
  Recent results of NA61/SHINE on hadron production in inelastic p+p
interactions suggest that the deconfinement may also take place in these
reactions. However, in this case mean multiplicity of particles with non-zero
strange charge is smaller than one. Thus for the modeling of p+p interactions
the exact strangeness conservation has to be implemented in the SMES. This
extension of the SMES is presented in the paper.
