Strong-box

ByteGuy owns a strong-box secured by a lock with $n$ knobs. Each knob, and each of the $n$ bolts hidden inside the lock, can be in one of $p$ positions numbered $0$ to $p-1$, where $p$ is prime.

The lock opens exactly when every bolt is at position $0$.

Turning knob $i$ forward by one position (from $0$ to $1$, from $1$ to $2$, ..., and from $p-1$ back to $0$) rotates bolt $j$ by $c_{i,j}$ positions: if bolt $j$ was at position $l$, it moves to $(l + c_{i,j}) \bmod p$.

ByteGuy has forgotten the combination. A 3D scanner lets him read the current position of every hidden bolt, and the lock is built so that exactly one final knob configuration opens it.

Given the current knob positions, the current bolt positions, and the coupling values $c_{i,j}$, output the knob configuration that opens the lock.

The first line contains two integers: the number of knobs $n$ with $1 \le n \le 300$, and the prime number of positions $p$ with $3 \le p \le 40000$.

The second line contains $n$ integers in the range $0 \ldots p-1$: the current positions of the knobs.

The third line contains $n$ integers in the range $0 \ldots p-1$: the current positions of the bolts.

Each of the next $n$ lines describes one knob. Line $i$ contains $n$ integers $c_{i,0}, c_{i,1}, \ldots, c_{i,n-1}$ with $0 \le c_{i,j} < p$.

Output one line with $n$ integers in the range $0 \ldots p-1$, separated by single spaces: the final knob positions that open the lock.