  The real and imaginary parts of the $K_L-K_S$ mixing matrix receive
contributions from all three charge-2/3 quarks: up, charm and top. These give
both short- and long-distance contributions which are accessible through a
combination of perturbative and lattice methods. We will discuss a strategy to
compute both the mass difference, $\Delta M_K$ and $\epsilon_K$ to sub-percent
accuracy, looking in detail at the contributions from each of the three CKM
matrix element products $V_{id}^*V_{is}$ for $i=u, c$ and $t$ as described in
Ref. [1]
