Problem E
Image Processing

Image editing software like Photoshop provide many image effects like blur, sharpen, and edge detection. These effects are commonly implemented through a kernel, a matrix describing a certain image effect. The kernel is applied to an image through convolution: flipping both the rows and columns of the kernel and then multiplying locationally similar entries and summing.

For example, let’s say we have the $4 \times 4$ image $ \begin{bmatrix} a & b & c & d \\ e & f & g & h \\ i & j & k & l \\ m & n & o & p \end{bmatrix} $ and the $2 \times 2$ kernel $ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}. $

After convolution, the resulting $3 \times 3$ image would be:

A real-world example of this is the blur effect:

Input

The first line of the input contains four integers, $H$, the height of the image, $W$, the width of the image, $N$, the height of the kernel, and $M$, the width of the kernel ($1 \leq H \leq 20$, $1 \leq W \leq 20$, $1 \leq N \leq H$, $1 \leq M \leq W$).

Each of the next $H$ lines contains $W$ integers, between $0$ and $100$ inclusive, representing the image.

Each of the next $N$ lines contains $M$ integers, between $0$ and $100$ inclusive, representing the kernel.

Output

Output the resulting image after convolution, consisting of $H-N+1$ lines, each with $W-M+1$ integers.

4 4 2 2
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
1 2
3 4

26 36 46
66 76 86
106 116 126