P5185 [COCI 2009/2010 #3] PLANETE

**Translated from [COCI 2009.12](http://hsin.hr/coci/archive/2009_2010/) T6 “[PLANETE](http://hsin.hr/coci/archive/2009_2010/contest3_tasks.pdf)”.** You are given $N$ records. The $i$-th record contains two dates $A_i, B_i$ **without a year** (in other words, only month and day), and an array $a_{i,1}, a_{i,2}, \dots, a_{i,M}$ of length $M$. Find any solution to the system of equations in $x_1, x_2, \dots, x_M\ (1 \le x_j \le 365)$: $\begin{cases}A_1+\displaystyle\sum_{j=1}^M a_{1,j}x_j\equiv B_1\pmod{365} \\ A_2+\displaystyle\sum_{j=1}^M a_{2,j}x_j\equiv B_2\pmod{365} \\ \vdots \\ A_N+\displaystyle\sum_{j=1}^M a_{N,j}x_j\equiv B_N\pmod{365}\end{cases}$ If there is no solution, output `-1` only.

The first line contains two integers $N, M$. In the next $N$ lines, the $i$-th line starts with four integers, representing: the day of $A_i$, the month of $A_i$, the day of $B_i$, and the month of $B_i$. Then follow $M$ integers representing $a_{i,1}, a_{i,2}, \dots, a_{i,M}$.

If there is a solution, output $M$ lines in total. The $i$-th line contains one integer, representing $x_i$. If there is no solution, output `-1` only.

Constraints: $1 \le N, M \le 200$, $0 \le a_{i,j} \le 200$. The input months and days are guaranteed to be valid. Translated by ChatGPT 5