Two second-order quantities related to K meson mixing, $\varepsilon_{K}$ and $\Delta M_K$, are Standard Model observables that are highly sensitive to possible new physics. The RBC and UKQCD collaborations have presented results for $\Delta M_{K}$ with physical quark masses and the first lattice calculation of the long-distance part of $\varepsilon_{K}$. Utilizing new-generation computers and new lattice configurations with an inverse lattice spacing of $2.7\ \mathrm{GeV}$ and physical quark masses, we can extend this previous work to obtain more precise results.