332. In parallelogram $ABCD$, which is not a rhombus, the ratio of the lengths of the diagonals is given as $AC: BD = k$. Let ray $AM$ be symmetric to ray $AD$ with respect to line $AC$, and ray $BM$ be symmetric to ray $BC$ with respect to line $BD$, with $M$ being the common point of rays $AM$ and $BM$. Find the ratio $AM: BM$.

333*. On a circle, $3k$ points are marked, dividing it into $3k$ arcs, of which $k$ arcs have length 1, another $k$ arcs have length 2, and the remaining $k$ arcs have length 3. Prove that among the marked points, there are two diametrically opposite points.
332. Answer: $M A / M B=k^{2}$. Let $O$ be the center of the parallelogram. Triangles $A O M$ and $M O B$ are similar.