Theater Seating [Rob Kolstad, 2010]

The cows have built an amphitheater with seats in the form of a
rectangle with *odd* width W (11 <= W <= 101) and with R rows (4
<= R <= 50) of seats. The distance between two adjacent seats on
the same row is the same as the distance between a pair of seats
that are in front of/behind each other on adjacent rows.

The cows wish to sell tickets over the internet and have automatic
seating assignment for each ticket they sell.

Ticket purchasers always want the best seat, so every seat has a
unique 'priority' associated with it (even if some seats might
appear to the layman to have the same priority). The middle seat
of the first row (which is closest to the stage) is located at
1,(W+1)/2 and has the very best priority. The closest seats (euclidean
distance!) to it have the next set of best values. The next closest
seats have slightly worse values, and so on.

All seats of equal distance on the first row are better than all
seats of that same distance on the second row (and so on).

Since some seats are equidistant from the best seat, those on the
same row that are closest to seat number 1 (the left-most seat when
the seats are viewed from the stage) are given better priority (see
the diagram below).

Here's a diagram of a small (11 x 5) theater where the seat's
'priority' is shown with #1 being the best:

                      Seat Number
            1  2  3  4  5  6  7  8  9 10 11
         +----------------------------------
   Row 5 | 54 50 44 38 32 29 33 39 45 51 55
   Row 4 | 52 42 34 25 21 18 22 26 35 43 53
   Row 3 | 48 36 23 14 12  9 13 15 24 37 49
   Row 2 | 46 30 19 10  5  4  6 11 20 31 47
   Row 1 | 40 27 16  7  2  1  3  8 17 28 41

Write a program that prints the seating priority chart for a supplied
width and row count.

PROBLEM NAME: tseat

INPUT FORMAT:

* Line 1: Two space-separated integers: W and R

SAMPLE INPUT (file tseat.in):

11 5

OUTPUT FORMAT:

* Lines 1..R: Line i contains W space-separated integers that are the
        seating priorities for row R-i+1

SAMPLE OUTPUT (file tseat.out):

54 50 44 38 32 29 33 39 45 51 55
52 42 34 25 21 18 22 26 35 43 53
48 36 23 14 12 9 13 15 24 37 49
46 30 19 10 5 4 6 11 20 31 47
40 27 16 7 2 1 3 8 17 28 41