  Let $\mathcal{A}$ be a finite set of integers, and let $h\mathcal{A}$ denote
the $h$-fold sumset of $\mathcal{A}$. Let $(h\mathcal{A})^{(t)}$ be subset of
$h\mathcal{A}$ consisting of all integers that have at least $t$
representations as a sum of $h$ elements of $\mathcal{A}$. The structure of the
set $(h\mathcal{A})^{(t)}$ is completely determined for all $h \geq h_t$.
