Sacred Scarecrows

Nerissa owns a rectangular paddy field of size $R \times C$. The field is divided into $R$ rows and $C$ columns of equal square cells. Each cell is either empty soil that can hold a scarecrow or soil already planted with rice.

To keep birds such as crows and sparrows away from the crops, Nerissa wants to place scarecrows on the field. A scarecrow can stand only on an empty cell. To keep other people from stealing the crops, the placement must be sacred. A placement is sacred when it satisfies both conditions below:

• Every row contains at least one scarecrow.
• Every pair of consecutive columns contains at least one scarecrow.

Two placements differ when some cell holds a scarecrow in exactly one of them. Count the distinct sacred placements.

The first line contains two integers $R$ and $C$ ($1 \le R \le 14$, $1 \le C \le 1000$), the number of rows and the number of columns. The next $R$ lines describe the field. Each line contains a string of length $C$. Each cell is written as . for empty soil or v for soil planted with rice.

Print the number of distinct sacred placements on one line. The number can be very large, so print it modulo $1,000,000,007$.

In the second sample case, 5 placements satisfy both conditions. With one row of three empty cells, 5 nonempty subsets cover both adjacent column pairs.

In the third sample case, the first row has no cell that can hold a scarecrow. Since every row needs at least one scarecrow, no sacred placement exists.

In the fifth sample case, 5 placements satisfy both conditions. The empty cells of the two rows are offset, so the row requirement and the column pair requirement together leave 5 possibilities.