CZ-SK-MO 2002 Problem 6

Let $\mathbb{R}^{+}$ denote the set of positive real numbers. Find all functions $f : \mathbb{R}^{+} \to \mathbb{R}^{+}$ satisfying for all $x, y \in \mathbb{R}^{+}$ the equality $$f(xf(y))=f(xy)+x$$