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Type II supernovae (SNe) interacting with disklike circumstellar matter (CSM) have been suggested as an explanation of some unusual Type II SNe, e.g., the so-called "impossible" SN, iPTF14hls. There are some radiation hydrodynamics simulations for such SNe interacting with a CSM disk. However, such disk interaction models so far have not included the effect of the ionization and recombination processes in the SN ejecta, i.e., the fact that the photosphere of Type IIP SNe between $\sim 10$-$\sim 100$ days is regulated by the hydrogen recombination front. We calculate light curves for Type IIP SNe interacting with a CSM disk viewed from the polar direction, and examine the effects of the disk density and opening angle on their bolometric light curves. This work embeds the shock interaction model of Moriya, et al. (2013) within the Type IIP SN model of Kasen & Woosley (2009), for taking into account the effects of the ionization and recombination in the SN ejecta. We demonstrate that such interacting SNe show three phases with different photometric and spectroscopic properties, following the change in the energy source: First few tens days after explosion (Phase 1), $\sim 10 - \sim 100$ days (Phase 2) and days after that (Phase 3). From the calculations, we conclude that such hidden CSM disk cannot account for overluminous Type IIP SNe. We find that the luminosity ratio between Phase 1 and Phase 2 has information on the opening angle of the CSM disk. We thus encourage early photometric and spectroscopic observations of interacting SNe for investigating their CSM geometry.