A really odd story but the idea and plot are one of a kind. A girl who has a crush on a guy she has never spoken too and sees him be crushed by an oncoming train. In her despair she is called to the past where her first interaction with people is a fight between the guy who just died and an evil villain. Through this she realizes her and her past self are one in the same and she is sent back to the future where she is able to save him from an untimely death.
Mahoroba no Yobigoe