2014 Cayley Problem 20

If wxyz is a four-digit positive integer with w \neq 0, the *layer sum* of this integer equals wxyz + xyz + yz + z. For example, the layer sum of 4089 is 4089 + 089 + 89 + 9 = 4276. If the layer sum of wxyz equals 2014, what is the value of w + x + y + z?

\textbf{(A)}\ 12\quad \textbf{(B)}\ 15\quad \textbf{(C)}\ 11\quad \textbf{(D)}\ 13\quad \textbf{(E)}\ 10

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.