AMC 12 2009b Problem 22

Parallelogram $ABCD$ has area $1, 000, 000$. Vertex $A$ is at $(0,0)$ and all other vertices are in the first quadrant. Vertices $B$ and $D$ are lattice points on the lines $y = x$ and $y = kx$ for some integer $k > 1$, respectively. How many such parallelograms are there?

\textbf{(A)}\ 49 \textbf{(B)}\ 720 \textbf{(C)}\ 784 \textbf{(D)}\ 2009 \textbf{(E)}\ 2048