  Given a pattern of length $m$ and a text of length $n$, the goal in
$k$-mismatch pattern matching is to compute, for every $m$-substring of the
text, the exact Hamming distance to the pattern or report that it exceeds $k$.
This can be solved in either $\widetilde{O}(n \sqrt{k})$ time as shown by Amir
et al. [J. Algorithms 2004] or $\widetilde{O}((m + k^2) \cdot n/m)$ time due to
a result of Clifford et al. [SODA 2016]. We provide a smooth time trade-off
between these two bounds by designing an algorithm working in time
$\widetilde{O}( (m + k \sqrt{m}) \cdot n/m)$. We complement this with a
matching conditional lower bound, showing that a significantly faster
combinatorial algorithm is not possible, unless the combinatorial matrix
multiplication conjecture fails.
