Looking for a functional satisfying $f(xf(y)) = \frac{f(x)}{y}$

I am looking for a functional $f:\mathbb{R}^*_+ \to \mathbb{R}^*_+$ satisfying:$$f(xf(y)) = \frac{f(x)}{y}.$$By replacing $x=y=1$ we get $f(f(1)) = f(1)$ but it does not give much information so $f \circ f=f$ kind of like $f(x)=\frac{1}{x}$ but it does not work.