  Some interaction-powered supernovae have long rise times of more than 100
days. We show that such long rise times are naturally expected if circumstellar
matters (CSM) have a flat density structure (s <~ 1.5, where rho_CSM ~ r^{-s}).
In such cases, bolometric luminosities from the CSM interaction keep increasing
as long as the CSM interacts with the outer layers of the SN ejecta. Thus, the
rise time is determined by the dynamical timescale in which the reverse shock
propagates the outer layers of the SN ejecta, not by the timescales in which
photons diffuse in the CSM as often considered. Interaction-powered supernovae
with very long rise times can be an important probe of extensive non-steady
mass loss in massive stars.
