RU-ALLRUSSIAN 2016 Problem 92

$\omega$ is a circle inside angle $\measuredangle BAC$ and it is tangent to sides of this angle at $B,C$ .An arbitrary line $\ell$ intersects with $AB,AC$ at $K,L$ ,respectively and intersect with $\omega$ at $P,Q$ .Points $S,T$ are on $BC$ such that $KS \parallel AC$ and $TL \parallel AB$ .Prove that $P,Q,S,T$ are concyclic.(I.Bogdanov,P.Kozhevnikov)