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 Rust (1.42.0) (judge verdict: Accepted)

#![allow(dead_code, unused_variables)]
use proconio::{fastout, input};
use proconio::marker::Chars;
use std::ops::*;
use std::mem::swap;
use std::fmt;

const MOD:usize = 1000000007;

#[fastout]
fn main() {
    input! {
        h:usize,
        w:usize,
        b : [Chars;h],
    }

    let mut dp :Vec<Vec<Modint>>= vec![vec![0.into();w];h];
    dp[0][0] = 1.into();
    for i in 0..h{
        for j in 0..w{
            if b[i][j] == '#'{
                continue;
            }

            if i == 0 && j == 0{
                continue
            }else if i == 0{
                dp[i][j] = dp[i][j-1];
            }else if j == 0{
                dp[i][j] = dp[i-1][j];
            }else{
                dp[i][j] = dp[i][j-1] + dp[i-1][j];
            }
        }
    }
    println!("{}",dp[h-1][w-1]);
}

#[derive(Copy,Clone)]
struct Modint{
    val : usize,
}

impl Modint{
    pub fn new(val : usize) -> Self{
        Modint{
            val : val%MOD,
        }
    }

    fn inv(&self) -> Self{
        let mut x : i32= 1;
        let mut u : i32= 0;
        let mut s : i32= self.val as i32;
        let mut t : i32= MOD as i32;

        while t != 0{
            let k = s/t;
            s -= k * t;
            swap(&mut s,&mut t);
            x -= k * t;
            swap(&mut x, &mut u);
        }
        x %= MOD as i32;
        if x < 0{
            x += MOD as i32;
        }
        
        let x = x as usize;
        Modint{
            val : x,
        }
    }
}

impl Add for Modint{
    type Output = Self;

    fn add(self, rhs: Self) -> Self {
        Self {
            val : (self.val + rhs.val) % MOD,
        }
    }
}

impl AddAssign for Modint {
    fn add_assign(&mut self, rhs: Modint) {
        *self = *self + rhs;
    }
}

impl Sub for Modint{
    type Output = Self;

    fn sub(self, other: Self) -> Self {
        Self {
            val :(MOD + self.val - other.val) % MOD,
        }
    }
}

impl SubAssign for Modint {
    fn sub_assign(&mut self, rhs: Modint) {
        *self = *self - rhs;
    }
}

impl Mul for Modint {
    type Output = Modint;

    fn mul(self, rhs: Modint) -> Self {
        Modint{
            val : (self.val * rhs.val) % MOD,
        }
    }
}

impl MulAssign for Modint {
    fn mul_assign(&mut self, rhs: Modint) {
        *self = *self * rhs;
    }
}

impl Div for Modint {
    type Output = Modint;

    fn div(self, rhs: Modint) -> Self {
        Modint{
            val : (self.val * rhs.inv().val) % MOD,
        }
    }
}

impl DivAssign for Modint {
    fn div_assign(&mut self, rhs: Modint) {
        *self = *self / rhs;
    }
}

impl From<i32> for Modint{
    fn from(x : i32) -> Self {
        let mut tmp = x;
        while tmp < 0{
            tmp += MOD as i32;
        }
        let res = Modint::new(tmp as usize);
        res
    }
}

impl From<usize> for Modint{
    fn from(x : usize) -> Self {
        let res = Modint::new(x);
        res
    }
}

impl fmt::Display for Modint{
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        write!(f, "{}", self.val)
    }
}