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;
#define int         long long
#define ull 		unsigned long long
#define ll 			long long
#define M 			1000000007
#define pb 			emplace_back
#define p_q 		priority_queue
#define pii         pair<ll,ll>
#define vi          vector<ll>
#define vii         vector<pii>
#define mi          map<ll,ll>
#define mii         map<pii,ll>
#define all(a)      (a).begin(),(a).end()
#define sz(x)       (ll)x.size()
#define endl        '\n'
#define gcd(a,b)    __gcd((a),(b))
#define lcm(a,b)    ((a)*(b)) / gcd((a),(b))
#define ios	    	ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define mp 			make_pair
#define lb 			lower_bound
#define ub			upper_bound
#define rep(i, begin, end) for (__typeof(end) i = (begin) - ((begin) > (end)); i != (end) - ((begin) > (end)); i += 1 - 2 * ((begin) > (end)))
#define ini(a,n,b)	for(ll int i=0;i<n;i++) a[i]=0;
#define cset(a)		__builtin_popcountll(a)
#define hell 		(ull)1e9
#define error(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); stringstream _ss(_s); istream_iterator<string> _it(_ss); err(_it, args); cerr<<endl; }
void err(istream_iterator<string> it) {}
template<typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
	cerr << *it << " = " << a << endl;
	err(++it, args...);
}

bool g[(ll)1e3+2][(ll)1e3+2];
int dp[(ll)1e3+2][(ll)1e3+2];
signed main(void)
{ios
	int h,w;
	cin>>h>>w;
	dp[1][1]=1;
	rep(i,1,h+1)
	rep(j,1,w+1)
	{
		char c;cin>>c;
		if(c=='#')
			g[i][j]=1;
	}
	rep(i,1,h+1)
	rep(j,1,w+1)
	{
		if(i==1&&j==1) continue;
		if(g[i][j]) continue;
		dp[i][j]=(dp[i-1][j]+dp[i][j-1])%M;
	}
	cout<<dp[h][w]<<endl;
}