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)

#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using ull=unsigned long long;
using pii=pair<ll,ll>;
#define For(i,a,b)  for(int i=a;i<=b;i++)
#define Forr(i,a,b) for(int i=a;i>=b;i--)
#define F first
#define S second
#define eb emplace_back
#define all(x) x.begin(),x.end()
#define sz(x) ((int)x.size())
#define bpc __builtin_popcount
#define MOD (ll)(1e9+7)
#define INF (2e9)
#define EPS (1e-6)
#define NATHANLEE_IS_EVIL_AND_ELECTRIC true
#define int ll
#ifdef LOCAL_TEST
#define debug(...) do{\
	cerr<<__PRETTY_FUNCTION__<<" - "<<__LINE__<<\
	" : ("#__VA_ARGS__<<") = ";\
	_OUT(__VA_ARGS__);\
}while(0)
template<typename T>void _OUT(T x){cerr<<x<<"\n";}
template<typename T,typename...I>void _OUT(T x,I ...tail){cerr<<x<<", ";_OUT(tail...);}
#else
#define debug(...)
#endif
void INIT(){
#ifdef LOCAL_TEST
	freopen("D:\\input.in","r",stdin);
	freopen("D:\\output.out","w",stdout);
	freopen("D:\\error.out","w",stderr);
#endif
	ios::sync_with_stdio(!NATHANLEE_IS_EVIL_AND_ELECTRIC);
	cin.tie(0);
}

ll gcd(ll a,ll b) { return b==0?a:gcd(b,a%b); }
ll lcm(ll a,ll b) { return a/gcd(a,b)*b; }
ll fpow(ll b,ll p){
	b%=MOD;
	ll ans=1;
	while(p>0){
		if(p&1) ans=(ans*b)%MOD;
		p/=2;
		b=(b*b)%MOD;
	}
	return ans;
}

char g[1010][1010];
int dp[1010][1010];

int32_t main() {
	INIT();
	//code...
	int n,m; cin>>n>>m;
	For(i,0,n) For(j,0,m){
		if(i==0 || j==0) g[i][j]='#';
		else cin>>g[i][j];
	}
	For(i,0,n) For(j,0,m){
		if(g[i][j]=='#') dp[i][j]=0;
		else if(i==1 && j==1) dp[i][j]=1;
		else dp[i][j]=dp[i-1][j]+dp[i][j-1];
		dp[i][j]%=MOD;
	}
	cout<<dp[n][m];
	return 0;
}