Density Map

You are given integers $n$ and $r$ with $n > r \ge 0$, together with an $n \times n$ table $F$ whose entries belong to $\{0, 1\}$. The columns and rows of the table are numbered from $1$ to $n$, and the value in column $i$, row $j$ is denoted $F[i, j]$.

The distance between two positions $[i, j]$ and $[i', j']$ is defined as $\max(|i - i'|,\ |j - j'|)$.

Compute the $n \times n$ table $W$, where $W[i, j]$ equals the sum of all entries $F[x, y]$ such that the distance between $[x, y]$ and $[i, j]$ is at most $r$.

Write a program that reads the integers $n$ and $r$ and the table $F$ from standard input, computes the table $W$, and writes it to standard output.

The first line contains two integers $n$ and $r$, separated by a single space, with $0 \le r < n \le 250$. Each of the next $n$ lines describes the table $F$ and contains $n$ integers from $\{0, 1\}$ separated by single spaces. The $i$-th number on the $(j+1)$-st line equals $F[i, j]$.

Print exactly $n$ lines. On the $j$-th line, print the values $W[1, j], W[2, j], \dots, W[n, j]$ in order, separated by single spaces.