Two points are chosen at random from the region bounded by the lines $x=0$, $y=0$, $x=1000$, and $y=1000$. These points are opposite corners of a rectangle with sides parallel to the axes. The expected value of the area of the rectangle can be expressed in the form $\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $a+b$.