Codeforces 348 D - Turtles Lindström–Gessel–Viennot lemma
#include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << "\n"; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 3e3 + 5; const int MOD = 1e9 + 7; int dp[N][N], n, m; char s[N][N]; int solve(int a, int b, int c, int d) { for (int i = 1; i <= n; ++i) for (int j = 1; j <= m; ++j) dp[i][j] = 0; for (int i = a; i <= c; ++i) { for (int j = b; j <= d; ++j) { if(i == a && j == b) { if(s[i][j] == '.') dp[i][j] = 1; } else { if(s[i][j] == '.') dp[i][j] = (dp[i-1][j]+dp[i][j-1])%MOD; } } } return dp[c][d]; } int main() { scanf("%d %d", &n, &m); for (int i = 1; i <= n; ++i) scanf("%s", s[i]+1); printf("%lld\n", (solve(1, 2, n-1, m)*1LL*solve(2, 1, n, m-1) - solve(1, 2, n, m-1)*1LL*solve(2, 1, n-1, m)%MOD+MOD)%MOD); return 0; }