Educational DP Contest AtCoder H - Grid 1

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Points: 7 (partial)
Time limit: 1.0s
Memory limit: 256M

Problem type

These problems are from the AtCoder DP contest, and were transferred onto DMOJ. All problem statements were made by several AtCoder users. As there is no access to the test data, all data is randomly generated. If there are issues with the statement or data, please open a ticket by clicking the "Report an issue" button at the bottom of the page.

There is a grid with horizontal rows and vertical columns. Let denote the square at the -th row from the top and the -th column from the left.

For each and . Square is described by a character . If is ., square is an empty square; if is #, square is a wall square. It is guaranteed that squares and are empty squares.

Taro will start from square and reach by repeatedly moving right or down to an adjacent empty square.

Find the number of Taro's paths from square to . As the answer can be extremely large, find the count modulo .

Constraints

• and are integers
• is . or #
• Squares and are empty squares

Input Specification

The first line will contain 2 space separated integers, and .

The next lines will each contain characters, either a . or #.

Output Specification

Print the number of Taro's paths from square to , modulo .

Sample Input 1

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

Sample Output 1

3

Explanation For Sample 1

There are three paths as follows:

Sample Input 2

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

Sample Output 2

0

Explanation For Sample 2

There may be no paths.

Sample Input 3

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

Sample Output 3

24

Sample Input 4

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

Sample Output 4

345263555

Explanation For Sample 4

Be sure to print the count modulo .