Let $S = \{ 1,2 , \ldots , n \}$. For any non-empty subset $A$ of $S$, let $l ( A )$ denote the largest number in $A$. If $f ( n ) = \sum _ { A \subseteq S } l ( A )$, that is, $f ( n )$ is the sum of the numbers $l ( A )$ while $A$ ranges over all the nonempty subsets of $S$, then $f ( n )$ is\\
(A) $2 ^ { n } ( n + 1 )$\\
(B) $2 ^ { n } ( n + 1 ) - 1$\\
(C) $2 ^ { n } ( n - 1 )$\\
(D) $2 ^ { n } ( n - 1 ) + 1$.