MEMO 2012 I1

Let $\mathbb{R} ^{+}$ denote the set of all positive real numbers. Find all functions $\mathbb{R} ^{+} \to \mathbb{R} ^{+}$ such that $$f(x+f(y)) = yf(xy+1)$$ holds for all $x, y \in \mathbb{R} ^{+}$ .