Shared code

#include <bits/stdc++.h>

using namespace std;

const int MN = 1005, MM = 12, MOD = 1e9 + 7;
int n, m, dp[MN][MM][1 << MM];

void add(int& a, int b) {
    a = (a + b) % MOD;
}

int32_t main() {

    cin >> m >> n;
    int full = (1 << (m + 1)) - 1; //the maximum possible mask with all m+1 bits set
    dp[0][m][0] = 1; //base case
    for (int i = 1; i <= n; i++) {
        for (int msk = 0; msk <= full; msk++) add(dp[i][0][msk << 1], dp[i - 1][m][msk]); //transfer data from row i-1 to i
        for (int j = 1; j <= m; j++) {
            for (int msk = 0; msk <= full; msk++) {
                int rit = msk & (1 << (j - 1)), dwn = msk & (1 << j); //right and down plug from (i, j-1) respectively
                if (!rit && !dwn) { //case 1
                    add(dp[i][j][msk ^ (1 << j)], dp[i][j - 1][msk]); //place right domino
                    add(dp[i][j][msk ^ (1 << (j - 1))], dp[i][j - 1][msk]); //place down domino
                } else if (rit && !dwn) add(dp[i][j][msk ^ (1 << (j - 1))], dp[i][j - 1][msk]); //case 2
                else if (!rit && dwn) add(dp[i][j][msk ^ (1 << j)], dp[i][j - 1][msk]); //case 3
            }
        }
    }
    printf("%d\n", dp[n][m][0]); //final answer

    return 0;
}