You guys are my one-and-only students!! How can I desert you?

Some guys are around the neighborhood beating people up and claiming that if they have any problem, they can go to Kurogin high. They also say that they are Hayato and Odagiri. One night the two were set up on a crime they didn't commit and the worst is no one believes them and the police officer wants them arrested. How will Yankumi find the impersonator and clear her students name?