Let \(\mathbb{R}^+\) denote the set of positive real numbers. Find all functions \(f: \mathbb{R}^+ \to \mathbb{R}^+\) such that for each \(x \in \mathbb{R}^+\), there is exactly one \(y \in \mathbb{R}^+\) satisfying

\[xf(y)+yf(x) \leq 2\]