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
.
If

and

are two positions in the table

, the distance between them is

.
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.