100541: [AtCoder]ABC054 B - Template Matching

Problem Statement

You are given an image $A$ composed of $N$ rows and $N$ columns of pixels, and a template image $B$ composed of $M$ rows and $M$ columns of pixels.
A pixel is the smallest element of an image, and in this problem it is a square of size $1×1$.
Also, the given images are binary images, and the color of each pixel is either white or black.

In the input, every pixel is represented by a character: . corresponds to a white pixel, and # corresponds to a black pixel.
The image $A$ is given as $N$ strings $A_1,...,A_N$.
The $j$-th character in the string $A_i$ corresponds to the pixel at the $i$-th row and $j$-th column of the image $A$ $(1≦i,j≦N)$.
Similarly, the template image $B$ is given as $M$ strings $B_1,...,B_M$.
The $j$-th character in the string $B_i$ corresponds to the pixel at the $i$-th row and $j$-th column of the template image $B$ $(1≦i,j≦M)$.

Determine whether the template image $B$ is contained in the image $A$ when only parallel shifts can be applied to the images.

Constraints

• $1≦M≦N≦50$
• $A_i$ is a string of length $N$ consisting of # and ..
• $B_i$ is a string of length $M$ consisting of # and ..

Input

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

$N$ $M$
$A_1$
$A_2$
$:$  
$A_N$
$B_1$
$B_2$
$:$  
$B_M$

Output

Print Yes if the template image $B$ is contained in the image $A$. Print No otherwise.

Sample Input 1

3 2
#.#
.#.
#.#
#.
.#

Sample Output 1

Yes

The template image $B$ is identical to the upper-left $2 × 2$ subimage and the lower-right $2 × 2$ subimage of $A$. Thus, the output should be Yes.

Sample Input 2

4 1
....
....
....
....
#

Sample Output 2

No

The template image $B$, composed of a black pixel, is not contained in the image $A$ composed of white pixels.