Sora o Miagete Omou Koto

In 2005 an artificial object flew into the Earth orbit. At the same time people with different supernatural powers started to appear on the planet. A research team was sent to the object and exploded together with the object.
In 2015 main character with the power of "possibility expansion" enrolls to a private school on a solitary island. This power helps to create the 3rd option when facing a fork. He communicates with teachers and students possessing different abilities without knowing that it's going to draw him closer to revealing the mystery of the space cube artificial object...

[From vndbreview]