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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

#define rep(i, n) for(ll i = 0; i < (ll)(n); i++)
template<typename T> void view(T cont) {std::cout << cont << std::endl;}
template<typename T> void view(T* cont, ll sz) {rep(i, sz) std::cout << cont[i] << " "; std::cout << std::endl;}
template<typename T> void view(const std::vector<T>& v) {for (const auto& f: v) std::cout << f << " "; std::cout << std::endl;}
template<typename T> void view(const std::vector<std::vector<T> >& vv) { for (const auto& v: vv) {view(v);}}
const long long INF = 1LL<<60;
template<class T> inline bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template<class T> inline bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

// Constraints
const int MAX_H = 1000;
const int MAX_W = 1000;
const int MOD = 1e9+7;

// Input
int H, W;
vector<vector<char> > a(MAX_H, vector<char>(MAX_W, ' '));
// DP table
vector<vector<int> > dp(MAX_H, vector<int>(MAX_W, 0));

void do_DP(int x, int y, int H, int W) {
    for (int i = 1; i < H; i++) {
        for (int j = 1; j< W; j++) {
            if (a[i][j] == '.') {
                dp[i][j] = (dp[i - 1][j] + dp[i][j - 1]) % MOD;
            } else {
                dp[i][j] = 0;
            }
        }
    }
}

int main(){
    cin >> H >> W;
    rep(i, H) {
        rep(j, W) {
            cin >> a[i][j];
        }
    }
    // Initialize dp table
    dp[0][0] = 1;
    for (int i = 1; i < MAX_H; i++) {
        if (a[i][0] == '#') {
            dp[i][0] = 0;
        } else {
            dp[i][0] = dp[i - 1][0];
        }
    }
    for (int j = 1; j < MAX_W; j++) {
        if (a[0][j] == '#') {
            dp[0][j] = 0;
        } else {
            dp[0][j] = dp[0][j - 1];
        }
    }

    // for (int i = 0; i < H; i++) {
    //     for (int j = 0; j < W; j++) {
    //         cout << dp[i][j] << " ";
    //     }
    //     cout << endl;
    // }
    do_DP(0, 0, H, W);
    // for (int i = 0; i < H; i++) {
    //     for (int j = 0; j < W; j++) {
    //         cout << dp[i][j] << " ";
    //     }
    //     cout << endl;
    // }
    cout << dp[H-1][W-1] << endl;
    // cout << "The number of path: " << path_number << endl;
}