CMO 1988 Problem 5

If $S$ is a sequence of positive integers let $p(S)$ be the product of the members of $S$ . Let $m(S)$ be the arithmetic mean of $p(T)$ for all non-empty subsets $T$ of $S$ . Suppose that $S'$ is formed from $S$ by appending an additional positive integer. If $m(S) = 13$ and $m(S') = 49$ , find $S'$ .