Grid

Title

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 ≤ i ≤ H, 1 ≤ j ≤ W), Square (i, j) is described by a character ai, j. If ai, j is ., Square (i, j) is an empty square; if ai, 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 109 + 7.

Constraints

  • H and W are integers.
  • 2 ≤ H, W ≤ 1000
  • ai, 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
a1, 1\ldotsa1, W
:
aH, 1\ldotsaH, W

Output

Print the number of Taro's paths from Square (1, 1) to (H, W), modulo 109 + 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 109 + 7.


Compile Errors


							
Time Limit: 1 Seconds
Memory Limit: 1024MB
No. of ACs: 59
Your best score: 0
Source: Atcoder Educational DP Contest

Subtask Score
1 100
2 0