Problem Description

Input Format

There will be multiple data sets for this problem. The first line of each data set will be two integers giving the height and width of the room. (We'll visualize the room as if on a piece of paper, as drawn above.) Each dimension will be no more than 20. The next line will contain an integer n (0 < n <= 10) followed by n pairs of integers, each pair giving the location of a box as the distances from the top and the left walls of the room. The following lines will be of the form direction m, where direction is either down, left, up, right, or done and m is a positive integer. For example, left 2 would mean to try to move the right wall 2 spaces to the left. The "direction" done indicates that you are finished pushing this set of boxes around. There will be no integer m following the direction done, of course. The data sets are followed by a line containing 0 0.

Output Format

For each data set you are to produce one line of output of the form:

Data set d ends with boxes at locations (r1, c1) (r2, c2) ... (rn, cn).

where the (ri, ci) are the locations of the boxes given from top-to-bottom, left-to-right, (separated by one space) and d is the data set number (starting at 1).

12 16
7 1 13 3 2 6 2 6 4 6 6 7 6 8 9 
down 3
left 14
done
4 4
3 1 0 2 1 2 3
right 3 
up 2 
left 1 
done 
0 0

Data set 1 ends with boxes at locations (3,1) (3,2) (6,0) (6,1) (6,2) (7,2) (8,2).
Data set 2 ends with boxes at locations (0,2) (1,1) (1,2).