Remember me, Alice (Tough Ladies Series 1)

Delinquent. Bastard. Hopeless. Three words best to describe Xenon Caliber Sebastian. He hated his life too much to the point of giving up to death. But just when he was about to jump off from a cliff, he was welcomed with a puch from a mysterious white-haired girl who appeared out of nowhere. She left him dumbfounded, struck with her words.
Now that he had been wakened up and decided to continue his life for the better and start a new, fate made their path crossed again.

But then, she can't recognize him.
Alice can't remember saving a suicidal guy on that one gloomy day.