Maximum Product Multiple

Chef is given three numbers $A$, $B$ and $K$. Chef considers an integer $x$ valid, that satisfies these conditions: - $x$ is a multiple of $K$, i.e. $x \; \% \; K = 0$ - $x$ ∈ [$A$, $B$] - $\forall \; d_i \; \exists \; d_j \; (d_i \; \% \; d_j = 0)$ where $0 \leq i < j \leq len(x) - 1$, where $len(x)$ denotes the number of digits in decimal representation of $x$ and $d_i$ denotes the $i$-th m