2004 AMC 10B Problem 19

In the sequence 2001, 2002, 2003, \ldots , each term after the third is found by subtracting the previous term from the sum of the two terms that precede that term. For example, the fourth term is 2001 + 2002 - 2003 = 2000. What is the 2004^\textrm{th} term in this sequence?

\mathrm{(A) \ } -2004 \qquad \mathrm{(B) \ } -2 \qquad \mathrm{(C) \ } 0 \qquad \mathrm{(D) \ } 4003 \qquad \mathrm{(E) \ } 6007

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