One day, people awoke to find themselves with the superhuman ability called Dialecte. They gathered in the academy city "Canaan" that was isolated from the general public - a futuristic town floating in the sky. Masaki was a high school student who had a peaceful hobby of making pastries and yet he was judged to have the peerless ability "Glow Verbaliser" so changed schools. He meets up with his childhood friend Shirley along with the quiet and mysterious Alice. The two of them are the strongest "Breaker" pair who supervise the rule-breakers of the school regulations regarding the misuse of illusions...but they break up over a trivial argument. Furthermore, since Masaki has the power that's called peerless, Alice chooses him as her new partner. The strongest! The unluckiest? Let's raise the curtain on the maximum level of tea and sweets superpower school battle!! (Source: Baka-Tsuki)