$K^0$ decays as analyzer of $B^0$ decays: How to measure the sign of $\Delta m_B$

We consider decays of neutral $B$ mesons with production of neutral $K$ mesons. They allow the use of oscillations of both $b$ flavor and strangeness simultaneously. New effects arising can be used to find $B$-decay parameters, in particular, signs of $\Delta m_B$ and $\Delta {\Gamma }_B$. Discrimination between effectively small and large $\mathrm{CP}$ violation is discussed. It is shown that secondary decay distributions themselves may be used to extract parameters of the primary $B$ decay.