Problem Statement

We have a grid with $H$ horizontal rows and $W$ vertical columns of squares. Square $(i,j)$, which is at the $i$-th row from the top and $j$-th column from the left, is wall if $S_{ij}$ is # and road if $S_{ij}$ is ..

There is a queen, the chess piece, at Square $(1, 1)$. In one move, it can move any number of squares to the right, downwards, or diagonally to the lower right to a road square without jumping over wall squares.

In how many ways can the queen travel from Square $(1, 1)$ to Square $(H, W)$? Find the count modulo $(10^9+7)$.

Here, two ways to travel are considered different if and only if there exists $i$ such that the position of the queen after the $i$-th move is different in those two ways.

Constraints

• $2 \leq H,W \leq 2000$
• $S_{ij}$ is # or ..
• $S_{11}$ and $S_{HW}$ are ..

Input

Input is given from Standard Input in the following format:

H W
S_{11}\ldots S_{1W}
\vdots
S_{H1}\ldots S_{HW}

Output

Print the number of ways, modulo $(10^9+7)$, in which the queen can travel from Square $(1, 1)$ to Square $(H, W)$.