2007 Pascal Problem 15

Clara knocks over the two stacks of blocks shown in the diagram. She then uses the blocks to build a similar stack whose top layer has one block and each layer below has one more block than the layer above it. If she builds the largest possible stack, how many blocks will be left over?

\textbf{(A)}\ 0\quad \textbf{(B)}\ 1\quad \textbf{(C)}\ 2\quad \textbf{(D)}\ 3\quad \textbf{(E)}\ 4

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 Pascal contests here.