Travel around China

Rikka is a rich girl.

She would like to visit the beautiful cities of China. The city locations in China can be simply regarded as a grid with $n$ rows and $m$ columns. Rows are numbered from $1$ to $n$ from north to south, and columns are numbered from $1$ to $m$ from west to east. The city in row $i$ and column $j$ is called $(i, j)$.

City $(i, j)$ has a direct expressway to city $(x, y)$ if and only if $|i - x| + |j - y| = 1$. Because New Year is coming, the expressways are open to the public free of charge.

When Rikka travels from city $(i, j)$ to $(x, y)$, she can only use expressways. The cost of a route is the sum of the costs of all cities she visits, including the starting and ending cities. If the route includes city $(i, j)$, she spends $a_{i, j}$ yuan. If she visits city $(i, j)$ a total of $k$ times, she spends $k \cdot a_{i, j}$ yuan, because there are always enough shopping malls for her to spend money.

Rikka is a fanciful girl, and she does not even pick a starting and ending city. Let $f(i, j, x, y)$ be the minimal cost of a route from city $(i, j)$ to city $(x, y)$. She wants the value

$\sum_{i=1}^{n} \sum_{x=1}^{n} \sum_{j=1}^{m} \sum_{y=1}^{m} [(i, j) \neq (x, y)] f(i, j, x, y)$

Since the answer may be very large, output it modulo $10^9 + 7$.

The first line contains two integers $n$ and $m$.

Each of the following $n$ lines contains $m$ integers. The $j$-th number in the $i$-th line is $a_{i, j}$.

It is guaranteed that $n = 3$, $1 \le m \le 1.5 \cdot 10^5$, and $1 \le a_{i, j} \le 10^9$.

Output a single integer, the answer modulo $10^9 + 7$.