PL-OM 2016 Problem 6

Let $I$ be an incenter of $\triangle ABC$ . Denote $D, \ S \neq A$ intersections of $AI$ with $BC, \ O(ABC)$ respectively. Let $K, \ L$ be incenters of $\triangle DSB, \ \triangle DCS$ . Let $P$ be a reflection of $I$ with the respect to $KL$ . Prove that $BP \perp CP$ .