  A modified Kardar-Parisi-Zhang (KPZ) equation is introduced, and solved
exactly in the infinite-range limit. In the low-noise limit the system exhibits
a weak-to-strong coupling transition, rounded for non-zero noise, as a function
of the KPZ non-linearity. The strong-coupling regime is characterised by a
double-peaked height distribution in the stationary state. The nonstationary
dynamics is quite different from that of the stationary state.
