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
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Sample Output 4
345263555
Explanation For Sample 4
Be sure to print the count modulo .
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