Rectangle A B C D has area 2006. An ellipse with area 2006 \pi passes through A and C and has foci at B and D. What is the perimeter of the rectangle? (The area of an ellipse is \pi a b, where 2 a and 2 b are the lengths of its axes.)
Answer Choices
A. \dfrac{16 \sqrt{2006}}{\pi}
B. \dfrac{1003}{4}
C. 8 \sqrt{1003}
D. 6 \sqrt{2006}
E. \dfrac{32 \sqrt{1003}}{\pi}