RU-SPB 2012 Problem 96

$ABC$ is triangle. Point $L$ is inside $ABC$ and lies on bisector of $\angle B$ . $K$ is on $BL$ . $\angle KAB=\angle LCB= \alpha$ . Point $P$ inside triangle is such, that $AP=PC$ and $\angle APC=2\angle AKL$ . Prove that $\angle KPL=2\alpha$