After creating problem Q, we thought it would be entertaining to put you into problemsetters’ shoes for a moment. In this task you will find out a way to create test data for problem Q.
Problem specification
You are given integers R, C, and A such that A divides RC.
Your task is to take a R × C rectangle and divide it into polygons. Each of the polygons must consist of exactly A unit squares. All polygons must be distinct, except for two polygons that must be identical.
Note: We call two polygons identical iff one of them can be obtained from the other by a combination of translations and rotations. Note that it is not allowed to use axis symmetry – i.e., if a polygon is just a mirror image of another one, they are considered distinct for the purpose of this problem.
Input specification
The input contains a single line with the three integers R, C, and A.
Output specification
After you divide the rectangle into N = RC∕A polygons, number them from 1 to N (in any order you wish).
Output R rows with C integers in each of them. The cth integer in the rth row must be the number of the polygon that contains the cell (r,c).
Any valid output will be accepted.
Example
input
5 6 5

output
1 1 2 2 2 3
1 4 4 2 2 3 1 1 4 3 3 3 6 6 4 4 5 5 6 6 6 5 5 5 