Problem Statement

You are given a prime number $p$ and an $N \times N$ matrix $A = (A_{i,j})$ ($1\leq i,j\leq N$). Each element of $A$ is an integer between $0$ and $p-1$, inclusive.

Consider a matrix $B$ obtained by replacing each zero in $A$ with an integer between $1$ and $p-1$, inclusive. There are $(p-1)^K$ such matrices $B$, where $K$ is the number of zeros in $A$.

Find each element, modulo $p$, of the sum of $B^p$ over all possible $B$.

Constraints

• $1 \leq N \leq 100$
• $p$ is a prime such that $1 \leq p \leq 10^9$.
• $0 \leq A_{i,j} \leq p-1$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N p
A_{1,1} \cdots A_{1,N}
\vdots
A_{N,1} \cdots A_{N,N}

Output

Print $N$ lines.

The $i$-th line should contain, in the order $j=1,\ldots,N$, the $(i,j)$ element of the sum, modulo $p$, of $B^p$ over all possible $B$, separated by spaces.