  We present a calculation of the connected-diagram contributions to the first
three non-trivial Mellin moments for the pion and kaon, extracted using local
operators with up to 3 covariant derivatives. We use one ensemble of gauge
configurations with two degenerate light, a strange and a charm quark
($N_f$=2+1+1) of maximally twisted mass fermions with clover improvement. The
ensemble has a pion mass $\sim$260 MeV, and a kaon mass $\sim$530 MeV. We
reconstruct the $x$-dependence of the PDFs via fits to our results, and find
that our lattice data favor a $(1-x)^2$-behavior in the large-$x$ region for
both the pion and kaon PDFs. We integrate the reconstructed PDFs to extract the
higher moments, $\langle x^n \rangle$, with $4 \leq n \leq 6$. Finally, we
compare the pion and kaon PDFs, as well as the ratios of their Mellin moments,
to address the effect of SU(3) flavor symmetry breaking.
