KMO 2020 Problem 2

$H$ is the orthocenter of an acute triangle $ABC$ , and let $M$ be the midpoint of $BC$ . Suppose $(AH)$ meets $AB$ and $AC$ at $D,E$ respectively. $AH$ meets $DE$ at $P$ , and the line through $H$ perpendicular to $AH$ meets $DM$ at $Q$ . Prove that $P,Q,B$ are collinear.