I just wanted to find this story

First I'm sorry if I have any errors since English is not my native language and I had to use a translator to make this text. And thanks in advance for your patience to read my resume and help me find this manhua/manga.


OK. Few days ago I remembered some manga that I read long time ago but because I don't remember title, author or if it was full manga or just one shot I have a problem with finding it. I have whole situation from manga in my head and its driving me crazy!
It starts with a boy entering a new school and he is looking for a roommate, since in that school everyone has to be matched to a roommate who will be his partner in everything, the grades are even combined.
The boy after discovering this rule went around the school campus looking for a partner and ends up bumping into someone who does not know and falls to the ground. This guy helps him up and asks if he gets hurt, he falls in love and asks if the guy wants to share a room with him and be his partner. But what he doesn't know is that this guy is actually the super popular school board president and already has a roommate who is the school board vice president. He didn't know why he was young and why everyone who already has a partner wears a brooch with his partner's initials, but this guy had no brooch with him.
The fact that they have partners indicates that they should do everything together and, as I said before, also share the test scores and the various extra-curricular activities they are required to participate in. In the early days, the president, who was full of bad intentions with the newbie, takes him to live with him in his super chic room because he is part of the highest level of division that is A and lives in super chic rooms. But the freshman is not used to the extra activities and rigid system of the college and makes the president fall into group F where they must live in a crumbling house as far away as possible from the campus where classes take place. They move there since they are obliged, but the president, accustomed to the good lifestyle, overhauls the old house and makes it very new and tidy. And the vice president who already had a history with the president and is jealous of the freshman decides that everyone on the class council will live there too.

And it was only until then that I read this story, then lost it and never found it again. Please help me!. (=・ω・=)