Looking for manga name?

I read a manga on Onemanga before they closed, and now I can't remember the name, probably because it wasn't in english.

I remember the main character was a woman who worked at an antique store. In the first chapter, she was walking home and saw a big black dog. Next thing I remember is there was a man she didn't know in her house telling a guy at her door she 'already had a man', basically.

The guy is the dog, and is practically immortal. They have sex quite a bit, but she's pretty firm about not doing it while he's in dog form (full moon, I think).

The story was interesting, and the ending kinda sad. I was hoping to reread it, but I haven't turned anything up on google. ><