Help- I forgot the name

There was this bl manga, shounen ai and I’m pretty sure it was manhwa.
The cover is like this guy sitting playing a guitar and mc looking at him T_T
The art is suuuper pretty, I think the ml taller guy has like purple hair medium length?
So the plot is like the purple hair tall guy is an idol and it starts with him coming home with a little guy to screw, but then sees his lover and is all toxic to him. The story is pretty much him being super toxic and abusive and eventually mc that likes him gets over him, and now ml is chasing after him.
He confesses to him on stage when he’s performing, risking his career, and lover boy is all upset.
I think he traps him in a villa on an island too? Then mc hates him even more

Help does anyone know the name :’)