Black and White

A rectangle is cut into $H \times W$ squares of size $1 \times 1$, so it has $H$ rows and $W$ columns. Each square is painted black or white. Each color has probability 50%, and the squares are independent.

A subrectangle is built by choosing at least one row and at least one column, then keeping only the squares that lie in a chosen row and in a chosen column. The chosen rows do not have to be adjacent, and neither do the chosen columns. For example, in a $3 \times 5$ rectangle, choosing rows 1 and 3 together with columns 2, 4 and 5 keeps the six squares shown below.

Two subrectangles are different whenever the chosen set of rows differs or the chosen set of columns differs, even if the coloring that remains looks the same. A subrectangle whose squares are all black is a black subrectangle, and one whose squares are all white is a white subrectangle.

Compute the expected value of the number of black subrectangles times the number of white subrectangles.

The first line contains two integers $H$ and $W$, the size of the rectangle, separated by one space. ($1 \le H, W \le 10^3$)

Write the expected value as a reduced fraction $a/b$ and print $(a \times b^{-1}) \bmod 1000000007$. Here $b^{-1}$ is the multiplicative inverse of $b$ modulo $1000000007$. The answer exists for every input that satisfies the constraints.