Sweet Devil ~Negaigoto, Kanaemasuu~

Main character is a shy introvert with his life passing by uneventfully. One day he finds an old book in the library that triggers his meeting with a devil girl. The girl is ready to fulfill any wish, but says that protagonist only has 10 days to live, and it can't be changed. Protagonist does not want to die, but if it's inevitable, he desires to have as much sex with cute girls over these 10 days as possible.