5 concyclic points

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Let $A$ and $B$ are the tangency points of the line $l$ with the circles $k_1$ and $k_2$. A line $m$ intersects $k_1$ and $k_2$ at the points $C, D, E, F$ in this order. Let $M$ is the middle of $AB$. Intersection points of $CM$ and $DM$ with $k_1$ are $K$ and $L$ respectively. Intersection points of $EM$ and $FM$ with $k_2$ are $N$ and $P$ respectively. Prove that $K, L, M, N, P$ are concyclic.

(don't loose your time - the problem is too easy)