  We prove that if $A\subseteq \{ 1,2,\dots, N \}$ does not contain any
solution to the equation $x_1+\dots+x_k=y_1+\dots+y_k$ with distinct
$x_1,\dots,x_k,y_1,\dots,y_k\in A$, then $|A|\ll {k^{3/2}}N^{1/k}.$
