  In this paper, we present the study for the energy reservoir powering the
light curves (LCs) of PS1-12cil and SN 2012aa which are superluminous and
luminous supernovae (SNe), respectively. The multi-band and bolometric LCs of
these two SNe show unusual secondary bumps after the main peaks. The two-peaked
LCs cannot be explained by any simple energy-source models (e.g., the $^{56}$Ni
cascade decay model, the magnetar spin-down model, and the ejecta-circumstellar
medium interaction model). Therefore, we employ the $^{56}$Ni plus
ejecta-circumstellar medium (CSM) interaction (CSI) model, the magnetar plus
CSI model, and the double CSI model to fit their bolometric LCs, and find that
both these two SNe can be explained by the double CSI model and the magnetar
plus CSI model. Based on the modeling, we calculate the the time when the
shells were expelled by the progenitors: provided that they were powered by
double ejecta-shell CSI, the inner and outer shells might be expelled $\sim
0.2-3.6$ and $\sim 2-25$ years before the explosions of the SNe, respectively;
the shells were expelled $\sim 2-20$ years before the explosions of the SNe if
they were powered by magnetars plus CSI.
