A polynomial
P(x)=c_{2004} x^{2004}+c_{2003} x^{2003}+\cdots+c_{1} x+c_{0}
has real coefficients with c_{2004} \neq 0 and 2004 distinct complex zeros z_{k}=a_{k}+b_{k} i, 1 \leq k \leq 2004 with a_{k} and b_{k} real, a_{1}=b_{1}=0, and
\sum_{k=1}^{2004} a_{k}=\sum_{k=1}^{2004} b_{k}
Which of the following quantities can be a nonzero number?
Answer Choices
A. c_{0}
B. c_{2003}
C. b_{2} b_{3} \ldots b_{2004}
D. \sum_{k=1}^{2004} a_{k}
E. \sum_{k=1}^{2004} c_{k}