BALTIC-WAY 2000 Problem 1

Let $K$ be a point inside the triangle $A B C$. Let $M$ and $N$ be points such that $M$ and $K$ are on opposite sides of the line $A B$, and $N$ and $K$ are on opposite sides of the line $B C$. Assume that

$$\angle M A B=\angle M B A=\angle N B C=\angle N C B=\angle K A C=\angle K C A .$$

Show that $M B N K$ is a parallelogram.