A U$-$tube manometer is filled with liquids A and $B,$ which are immiscible with each other, as shown in the figure. The legs of the manometer have different diameters $D_1$ and $D_2.$ Densities of the liquids are given as ${}_A$ and ${}_B.$ If $mkg$ of $B$ is added to the leg $2,$ what would be the change in the level of the interface between liquid A and liquid B$?$ Express the level change in terms of the provided parameters.