Problem:
Score : 100 points

Problem Statement

There is a grid with H horizontal rows and W vertical columns.
Let (i, j) denote the square at the i-th row from the top and the j-th column from the left.

For each i and j (1 \leq i \leq H, 1 \leq j \leq W), Square (i, j) is described by a character a_{i, j}.
If a_{i, j} is ., Square (i, j) is an empty square; if a_{i, j} is #, Square (i, j) is a wall square.
It is guaranteed that Squares (1, 1) and (H, W) are empty squares.

Taro will start from Square (1, 1) and reach (H, W) by repeatedly moving right or down to an adjacent empty square.

Find the number of Taro's paths from Square (1, 1) to (H, W).
As the answer can be extremely large, find the count modulo 10^9 + 7.

Constraints

H and W are integers.

2 \leq H, W \leq 1000

a_{i, j} is . or #.

Squares (1, 1) and (H, W) are empty squares.

Input

Input is given from Standard Input in the following format:

H W
a_{1, 1}\ldotsa_{1, W}
:
a_{H, 1}\ldotsa_{H, W}

Output

Print the number of Taro's paths from Square (1, 1) to (H, W), modulo 10^9 + 7.

Sample Input 1

3 4
...#
.#..
....

Sample Output 1

3

There are three paths as follows:

Sample Input 2

5 2
..
#.
..
.#
..

Sample Output 2

0

There may be no paths.

Sample Input 3

5 5
..#..
.....
#...#
.....
..#..

Sample Output 3

24

Sample Input 4

20 20
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................

Sample Output 4

345263555

Be sure to print the count modulo 10^9 + 7.

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE BangPatterns #-}
import Control.Arrow
import Control.Monad.Fix
import Data.Int
import Data.Foldable
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import qualified Data.ByteString.Char8 as B
import Debug.Trace

iscanl :: (Int -> a -> b -> a) -> a -> V.Vector b -> V.Vector a
iscanl !k !a !v = V.scanl' (\(!x) (!i, !v) -> k i x v) a (V.indexed v)

iscanlU
  :: (VU.Unbox a, VU.Unbox b)
  => (Int -> a -> b -> a)
  -> a
  -> VU.Vector b
  -> VU.Vector a
iscanlU !k !a !v = VU.scanl' (\(!x) (!i, !v) -> k i x v) a (VU.indexed v)

solve :: Int -> Int -> V.Vector (VU.Vector Bool) -> Int32
solve !h !w !ahw = dp V.! h VU.! (w - 1)
 where
  add !x !y = (x + y) `mod` (10 ^ 9 + 7)

  dp :: V.Vector (VU.Vector Int32)
  dp = iscanl
    ( \(!i) (!acc) (!row) -> VU.tail $ iscanlU
      (\(!j) (!prev) (!ch) -> if ch then 0 else acc VU.! j `add` prev)
      0
      row
    )
    (VU.generate w (\(!i) -> if i == 0 then 1 else 0))
    ahw

main = do
  let readInt :: Integral a => B.ByteString -> Maybe (a, B.ByteString)
      readInt = fmap (first fromIntegral . second B.tail) . B.readInt

  (h, w) <-
    (\vec -> (vec VU.! 0, vec VU.! 1)) . VU.unfoldrN 2 readInt <$> B.getLine
  ahw <-
    V.replicateM h
    $   VU.unfoldrN w (\bs -> Just (B.head bs == '#', B.tail bs))
    <$> B.getLine
  print $ solve h w ahw