Clock Zero: Shuuen no ichibyou

Kurou Nadeshiko is the 12 year old daughter of some wealthy high class members. She goes to a wealthy school with her childhood friend where other rich kids go to. She hopes to one day become a doctor and every night she seems to have dreams about being in another world. The world is full of ruins and she herself is 10 years older. One day a transfer student named Kaido Takato comes to her class and she gets involved in an after school extra-curricular club which they call Clock Zero.