2010 AMC 12B Problem 14

Let a, b, c, d, and e be positive integers with a+b+c+d+e=2010 and let M be the largest of the sums a+b, b+c, c+d and d+e. What is the smallest possible value of M?

\textbf{(A)}\ 670 \qquad \textbf{(B)}\ 671 \qquad \textbf{(C)}\ 802 \qquad \textbf{(D)}\ 803 \qquad \textbf{(E)}\ 804

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.