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 C++ (GCC 9.2.1) (judge verdict: Accepted)

// CODE © by 𝕌𝕥𝕜𝕒𝕣𝕤𝕙 𝔾𝕒𝕣𝕘
// Copying or sharing of this code without permission of the Author is strictly prohibited!!!
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define Speed ios::sync_with_stdio(0); cin.tie(0);
#define pb push_back
#define endl "\n"
int arr[1001][1001], dp[1001][1001];
const int mod = 1e9 + 7;
int f(int i, int j, int n, int m) {
	// cout << "at " << i << " " << j << "avl is " << arr[i][j] << endl;
	if (i == n - 1 && j == m - 1) {return 1;}
	if (i == n || i < 0 || j == m || j < 0 || arr[i][j] == -1)return 0;
	int ans = 0;
	if (i < n - 1 && dp[i + 1][j] != -1)ans = (ans + dp[i + 1][j]) % mod;
	else if (i < n - 1) {dp[i + 1][j] = f(i + 1, j, n, m); ans = (ans + dp[i + 1][j]) % mod;}
	if (j < m - 1 && dp[i][j + 1] != -1)ans = (ans + dp[i][j + 1]) % mod;
	else if (j < m - 1) {dp[i][j + 1] = f(i, j + 1, n, m); ans = (ans + dp[i][j + 1]) % mod;}
	return ans;
}
signed main() {
#ifndef ONLINE_JUDGE
	freopen("input.txt", "r", stdin);
	// freopen("output.txt", "w", stdout);
#endif
	int a = 0, b = 0, c = 0, d = 0, i = 0, j = 0, k = 0, t = 0, n = 0, q = 0, m;
	cin >> n >> m;
	memset(dp, -1, sizeof(dp));
	for (int i = 0; i < n; i++) {
		string s;
		cin >> s;
		for (int j = 0; j < m; j++)arr[i][j] = (s[j] == '.' ? 0 : -1);
	}
	// arr[n - 2][m - 1] = 1; arr[n - 1][m - 2] = 1;
	cout << f(0, 0, n, m);
}