European Space Agency has \(N\) telescopes observing distant planets. They classified \(M\) different types of events. They noticed that every day on each planet there is exactly one type of event. They measure events in days because they discovered each event lasts at least one day, and at most \(365\) days. Events last only complete number of days, they never last fractional part of a day. Each event of the same type lasts exactly the same number of days every time it occurs, regardless of the planet it occurs on.

After many years of observation they want to analyze data. The telescopes logged all observations, but unfortunately they forgot to write down the year the observations took place! Each telescope entry consists of start date, end date and number of each type of events observed. Given all observations on all planets, calculate the duration of each type of event. Note that the telescopes are super precise and they start working exactly when the event starts and end when an event ends, not necessarily the same one.

Note: for this task, each year has exactly \(365\) days.

First line contains integers \(N\) and \(M\) (\(1 \le N, M \le 200\)), number of telescopes and number of event types. Next \(N\) lines contain \(M+4\) numbers each:

$$ D_1 D_1\ M_1 M_1\ D_2 D_2\ M_2 M_2\ F_1\ F_2\ \ldots\ F_M $$

Where \(D_1 D_1\ M_1 M_1\) (\(01 \le DD \le 31\), \(01 \le MM \le 12\)) are the start date, \(D_2 D_2\ M_2 M_2\) the end date, and \(F_i\) (\(0 \le F_i \le 200\)) the number of times event type \(i\) was observed.

One line containing \(M\) numbers, durations of event types. If more than one solution exists, output any one. If no solution exists, output -1.

First sample description: Telescope observed one type \(1\) event between \(26\). February and \(3\). March. The only possible explanation is that type \(1\) events last \(5\) days.

riseoj 작성

출처 COCI 2009/2010 Contest 3