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"
#include <ext/pb_ds/assoc_container.hpp> 
using namespace __gnu_pbds; 
using namespace std;

#define double long double
#define int long long
#define pb push_back 
#define Z(c) (int)(c).size()
#define L(c) c[Z(c)-1]
#define F first
#define S second
#define nl "\n"
#define mii map<int,int> 
#define all(c) (c).begin(),(c).end()
#define rall(c) (c).rbegin(),(c).rend()
#define rep(i,iv,n) for(int (i)=(iv);(i)<(n);++(i))
#define FO fflush(stdout) 
#define D1(x) cerr <<"At line "<<__LINE__<<" "<<#x<<"="<<x<<nl
#define D2(x,y) cerr <<"At line "<<__LINE__<<" "<<#x<<"="<<x<<" "<<#y<<"="<<y<<nl
#define D3(x,y,z) cerr <<"At line "<<__LINE__<<" "<<#x<<"="<<x<<" "<<#y<<"="<<y<<" "<<#z<<"="<<z<<nl
#define tr(it,ct) for(auto &(it) : (ct))
#define pi acos(-1)
#define prt(ct) for(auto &(it) : (ct)) cerr<<it<<" "; cerr<<nl
#define prtp(ct) for(auto &(it) : (ct)) cerr<<it.F<<" "<<it.S<<nl; cerr<<nl

typedef vector< int > vi;
typedef vector< vi > vvi;
typedef pair< int,int > pii;
typedef vector< pii > vp;
typedef tree<int, null_type, less<int>, rb_tree_tag, 
             tree_order_statistics_node_update> baap;

void swap(char &a,char &b)
{ auto tm=a; a=b; b=tm; }

void mina(int &a,int b)
{ a=(a<b?a:b); }

void maxa(int &a,int b)
{ a=(a>b?a:b); }

  const int mod=1000000007;
  const int mod2=998244353;
  const int INF=1e16+18;
  const int N=1e5+15;
  const int M=1e3+13;

  int dp[M][M];

 void fft()              
 {
   int n,m; cin>>n>>m;
   string s[n]; rep(i,0,n) cin>>s[i];

   for(int i=0;i<n;++i){

     for(int j=0;j<m;++j)
      {
         if(i==0&&j==0) dp[i][j]=1;
         else if(s[i][j]=='#') dp[i][j]=0;
         else {
            if(i-1>=0) dp[i][j]=dp[i-1][j];
            if(j-1>=0) dp[i][j]+=dp[i][j-1];
            dp[i][j]%=mod;
         }
      }
   }

   cout<<dp[n-1][m-1];

 }

signed main()
{ 
   ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    
   int tc=1;                         
 //  cin>>tc;

  rep(i,1,tc+1)
  { // cout<<"Case #"<<i<<": ";
   fft();
   if(i<tc)
   cout<<nl;
  }
  
 return 0; 
}