4 8, 9 5, 3 1, 2 6, 
10, 7
| Problem 133 - The Dole Queue, Explanations |
It's the classical simulation problem except that there are two counts.
The two victims leave the ring simultaneously, so the choice of the second victim will not depend of the choice of the first victim.
In case of pairs, output the victim chosen by the counter-clockwise person first and do not ouput commas.
Problem 130 - Roman Roulette is really similar.
Problem 151 - Power Crisis is really similar.
If you are in trouble with the multi-entry input, read my how to read input.
In a serious attempt to downsize (reduce) the dole queue, The New National Green Labour Rhinoceros Party has decided on the following strategy. Every day all dole applicants will be placed in a large circle, facing inwards. Someone is arbitrarily chosen as number 1, and the rest are numbered counter-clockwise up to N (who will be standing on 1's left). Starting from 1 and moving counter-clockwise, one labour official counts off k applicants, while another official starts from N and moves clockwise, counting m applicants. The two who are chosen are then sent off for retraining; if both officials pick the same person she (he) is sent off to become a politician. Each official then starts counting again at the next available person and the process continues until no-one is left. Note that the two victims (sorry, trainees) leave the ring simultaneously, so it is possible for one official to count a person already selected by the other official.
Write a program that will successively read in (in that order) the three numbers (N, k and m; k, m > 0, 0 < N < 20) and determine the order in which the applicants are sent off for retraining. Each set of three numbers will be on a separate line and the end of data will be signalled by three zeroes (0 0 0).
For each triplet, output a single line of numbers specifying the order in which people are chosen. Each number should be in a field of 3 characters. For pairs of numbers list the person chosen by the counter-clockwise official first. Separate successive pairs (or singletons) by commas (but there should not be a trailing comma).
10 4 3 0 0 0
4 8, 9 5, 3 1, 2 6, 10, 7
where represents a space.