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Let \( A = \{0 = a_0 < a_1 < \cdots < a_{\ell + 1} = b\} \) be a finite set of non-negative integers. We prove that the sumset \( NA \) has a certain easily-described structure, provided that \( N \geqslant b-\ell \), as recently conjectured by Granville and Shakan. We also classify those sets \( A \) for which this bound cannot be improved.

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