2009 AMC 12B 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\qquad \textbf{(B)}\ 720\qquad \textbf{(C)}\ 784\qquad \textbf{(D)}\ 2009\qquad \textbf{(E)}\ 2048

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