RU-ALLRUSSIAN 1987 Problem 19

The set $\mathrm{S}_0 = \{1,2!4!8!16!,\ldots \}$ . The set $\mathrm{S}_{\mathrm{n + 1}}$ consists of all finite sums of distinct elements of $\mathrm{S}_{\mathrm{n}}$ . Show that there is a positive integer not in $\mathrm{S}_{1987}$ .