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 VIII Olimpiada Informatyczna 2000/2001

 Task: MAP Author: Tomasz Śmigielski
Density map

 I stage contest

There are given:

• integers n > r >= 0,
• F - the table n x n with the numbers from the set {0,1}; columns and lines of the table are numbered from 1 to n; the number in i-th column and j-th line of the table is denoted by F[i, j].

If [i, j] and [i', j'] are two positions in the table F, the distance between them is max(|i - i'|, |j - j'|).

The table W, n x n, should be computed, where W[i, j] (the number in i-th column and j-th line of the table W) is equal to the sum of all the numbers F[x,y], such that the distance between [x,y] and [i,j] is not greater than r.

Write a program, which:

• reads integers n, r and the table F from the text file MAP.IN,
• computes the table W,
• writes the table W into the text file MAP.OUT.

#### Input

In the first line of the text file MAP.IN there are two positive integers separated by a single space: n and r, where 0 <= r < n <= 250. In the following n lines the table F is described. Each of these lines contains n integers from the set {0,1}, separated by single spaces. The i-th number written in (j+1)-st line is equal to F[i, j].

#### Output

The text file MAP.OUT should contain exactly n lines. In the j-th line the values W[1, j]...W[n, j] should be written respectively; they should be separated by single spaces.

#### Example

For the input file MAP.IN:

```5 1
1 0 0 0 1
1 1 1 0 0
1 0 0 0 0
0 0 0 1 1
0 1 0 0 0
```

The correct answer is the output file MAP.OUT:

```3 4 2 2 1
4 5 2 2 1
3 4 3 3 2
2 2 2 2 2
1 1 2 2 2
```

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