Let $X$ be a complete metric space, let $M \subseteq X$ such that $X-M$ is a second category space prove that $M$ is first category space.
My attempt. We know that $X$ is complete metric space, so $X$ is a second category space, and also $$X=(X-M) \cup M,$$ I wanted to do it by contradiction but it doesn't get me anywhere, assuming that $M$ is a second category space.