RU-SPB 2014 Problem 117

$I$ - incenter , $M$ - midpoint of arc $BAC$ of circumcircle, $AL$ - angle bisector of triangle $ABC$ . $MI$ intersect circumcircle in $K$ . Circumcircle of $AKL$ intersect $BC$ at $L$ and $P$ . Prove that $\angle AIP=90$