HMIC 2018 Problem 4

Find all functions $f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$such that

$$f(x+f(y+x y))=(y+1) f(x+1)-1$$

for all $x, y \in \mathbb{R}^{+}$. ( $\mathbb{R}^{+}$denotes the set of positive real numbers.)