When the expression \left[(1+x)\left(1+2x^3\right)\left(1+4x^9\right)\left(1+8x^{27}\right)\left(1+16x^{81}\right)\left(1+32x^{243}\right)\left(1+64x^{729}\right)\right]^2 is expanded and simplified, the coefficient of x^{2003} is
Answer Choices
A. 0
B. 2^{28}
C. 2^{30}
D. 2^{29}
E. 2^{31}