TC VolleyballTournament

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Consider the vectors (0,3,0,1), (1,3,0,1), (2,3,0,1), (3,0,1,0), (3,1,1,0), (3,2,1,0). Your input is a 4D vector obtained by adding nonnegative integer multiples of these vectors. You are to determine how the multipliers were chosen, or whether they could have been chosen in more than one way.

From TopCoder Single Round Match 344.