Density Map

Memory limit: 32 MB

There are given:

• integers ,
• - the table with the numbers from the set ; columns and lines of the table are numbered from to ; the number in -th column and -th line of the table is denoted by .

The table , , should be computed, where (the number in -th column and -th line of the table ) is equal to the sum of all the numbers , such that the distance between and is not greater than .

Task

Write a program, which:

• reads integers , and the table from the standard input,
• computes the table ,
• writes the table to the standard output.

Input

In the first line of standard input there are two positive integers separated by a single space: and , where . In the following lines the table is described. Each of these lines contains integers from the set , separated by single spaces. The -th number written in -st line is equal to .

Output

The standard output should contain exactly lines. In the -th line the values should be written respectively; they should be separated by single spaces.

Example

For the input data:

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 result is:

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

Task author: Tomasz Smigielski.