AMC 12 2011b Problem 13

Brian writes down four integers $w > x > y > z$ whose sum is $44$. The pairwise positive differences of these numbers are $1, 3, 4, 5, 6$ and $9$. What is the sum of the possible values of $w$?

\textbf{(A)}\ 16 \textbf{(B)}\ 31 \textbf{(C)}\ 48 \textbf{(D)}\ 62 \textbf{(E)}\ 93