  We present calculations of the invariant mass spectra of the $\Lambda$p
system for the exclusive $p p \to K^+ \Lambda p$ reaction with the aim of
studying the final state interaction between the $\Lambda$-hyperon and the
proton. The reaction is described within a meson exchange framework and the
final state $\Lambda p$ interaction is incorporated through an off-shell
t-matrix for the $\Lambda p \to \Lambda p$ scattering, constructed using the
available hyperon-nucleon (YN) potentials. The cross sections are found to be
sensitive to the type of YN potential used especially at the $\Lambda$ and
$\Sigma$ production thresholds. Hence, data on this exclusive reaction, which
can be used to constrain the YN potentials are desirable.
