Let [Formula: see text] be a non-empty finite set of integers. For any integer [Formula: see text], let [Formula: see text]. One of the important problems in additive combinatorics is to find the optimal lower bound for the cardinality of the sumset [Formula: see text]. Cilleruelo, Silva, and Vinuesa conjectured that, if [Formula: see text] is a positive integer and [Formula: see text] is a finite set of integers with sufficiently large cardinality, then [Formula: see text]. For some values of [Formula: see text] this conjecture is already confirmed. In this article, under certain restrictions on set [Formula: see text], we confirm this conjecture for all positive integers [Formula: see text] except for those of the form [Formula: see text] or [Formula: see text] where [Formula: see text] is an odd prime number and [Formula: see text] for [Formula: see text].