KöMaL 2021 C1675

Let $D$ be an interior point of side $AB$ in triangle $ABC$, and $\frac{AD}{DB}=\frac{m}{n}<\frac{1}{2},$ where $m$, $n$ are positive integers. A point $E$, different from $D$, is marked on the circumference of the triangle such that line $DE$ divides the area of the triangle in a $1:2$ ratio. Depending on the numbers $m$ and $n$, on which side of the triangle will point $E$ lie, and in what ratio will it divide that side?