Let $E F G H$ be a convex quadrilateral, and $K, L, M, N$ be the midpoints of segments $E F, F G, G H, H E$ respectively; $O$ be the intersection point of segments $K M$ and $L N$. It is known that $\angle L O M = 90^{\circ}$, $K M = 3 L N$, and the area of quadrilateral $K L M N$ is $S$. Find the diagonals of quadrilateral $E F G H$.
The midpoints of the sides of any quadrilateral are the vertices of a parallelogram.

## Otвет

$2 \sqrt{\frac{5 S}{3}}, 2 \sqrt{\frac{5 S}{3}}$.