  We perform hydrodynamical simulations of the interaction between supernova
(SN) ejecta and circumstellar medium (CSM) for SN 1993J and SN 2011dh, and
calculate the radio and X-ray emissions expected from the shocked gas at late
epochs ($t$). Considering the ejecta structure from multi-group radiation
hydrodynamics simulation, we find that the observed rapid drop in radio and
X-ray light curves of SN 1993J at $t>$3000 days can be due to a change in the
mass-loss rate ($\dot M$) around $\sim$6500 years prior to the explosion of the
SN. The exact epoch scales inversely with the assumed wind velocity of $v_{\rm
w}=10~ km~s^{-1}$. The progenitor of this SN very likely belonged to a binary
system, where, during its evolution, the primary had transferred material to
the secondary. It is argued in the paper that the change in $\dot M$ can happen
because of a change in the mass accretion efficiency ($\eta$) of the companion
star. It is possible that before $\sim6500~(v_{\rm w}/10~km~s^{-1})^{-1}$years
prior to the explosion, $\eta$ was high, thus the CSM was tenuous, which causes
the late time downturn in fluxes. In the case of SN 2011dh, the late time
evolution is found to be consistent with a wind medium with $\dot M/v_{\rm
w}=4\times10^{-6 }~M_{\odot}~ yr^{-1}/10 ~{km ~s^{-1}}$. It is difficult from
our analysis to predict whether the progenitor of this SN had a binary
companion, however, if future observations show similar decrease in radio and
X-ray fluxes, then that would give strong support to a scenario where both SNe
had undergone similar kind of binary evolution before explosion.
