Smoothing is used to reduce noise within an image or to produce a less pixelated image. You have been given an image G of resolution N x N. Image will be represented as a $2D$ grid G of size N x N where $G_{i, j}$ will denote intensity of color in a grayscale image of pixel $(i,\;j)$.

You have been given a filter mask F of size $(2 * M + 1)$ x $(2 * M + 1)$. Using this filter mask, you have to perform smoothing operation on the G and output the final image $NewG$. Smoothing operation for any particular pixel $(i, \;j)$ can be described as:

$NewG_{i, j} = \sum_{p=-M}^{p=M} \sum_{q=-M}^{q=M} G_{i+p, j+q} * F_{p, q}$

In the above formula, if any pixel $(x,\;y)$ is situated outside of grid of size N x N, then $G_{x, y} = 0$.

INPUT:
First line of input will consists of two integers N and M. Next $2 * M + 1$ lines will consists of $2 * M + 1$ integers denoting filter mask F. $(M+1)^{th}$ integer on $(M+2)^{th}$ line will give the value of $F_{0, 0}$, first integer on second line will give the value of $F_{-M, -M}$ and last integer on $(2 * M + 2)^{th}$ line will give the value of $F_{M, M}$. Next N lines will consists of N integers denoting the image G.

OUTPUT:
Output the image $NewG$ obtained by smoothing the image G using filter mask F.

CONSTRAINTS
$2 \le N \le 100$
$1 \le M \le 10$
$0 \le G_{i,j}, F_{i,j} \le 100$