Ion Express

Sorohue wants to open the Ion Express in SCS City. There are $N^2$ stations arranged in an $N \times N$ grid. Station $(i,j)$ is in the $i$-th row from the top and the $j$-th column from the left.

Assign an integer from $1$ to $N$ to each station. Connect each pair of horizontally or vertically adjacent stations with one rail labeled + or -.

A route starts at station $(1,1)$, moves only right or down, and ends at station $(N,N)$. Its energy is the value of the expression obtained by concatenating the integers at its $2N-1$ stations and the operators on its $2N-2$ rails in traversal order. There is no operator before the integer at the starting station.

There are $K$ types of trains, requiring energies $E_1,E_2,\cdots,E_K$. Assign the station integers and rail operators so that, for every , at least one route has energy exactly . All trains use the same assignment, and their routes may overlap.

The input is given in the following format:

$N\ K$ $E_1\ E_2\ \cdots\ E_K$

If no valid assignment exists, print NO on the first line.

Otherwise, print YES on the first line, followed by:

• $N$ lines containing $N$ space-separated integers each. The $j$-th integer on the $i$-th line is the integer assigned to station $(i,j)$ and must be between and , inclusive.

• $5 \le N \le 100$.
• $1 \le K \le N^2$.
• ().