Problem:
Score : 200 points

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.

Solution in PHP7 (7.0.15) (judge verdict: Accepted)

<?php
/*
    Problem URL : http://abc054.contest.atcoder.jp/tasks/abc054_b

    Score  :
    Result :
    Time   : ms
    Memory : KB
 */

fscanf(STDIN, "%d %d", $N, $M);

for ($i = 0; $i < $N; $i++) {
    $mapN[$i] = str_split(trim(fgets(STDIN)));
}
for ($i = 0; $i < $M; $i++) {
    $mapM[$i] = str_split(trim(fgets(STDIN)));
}

for ($x = 0; $x <= $N - $M; $x++) {
    for ($y = 0; $y <= $N - $M; $y++) {
        // echo ("\$x = $x : \$y = $y\n");
        $bool = true;
        for ($i = 0; $i < $M; $i++) {
            for ($j = 0; $j < $M; $j++) {
                if ($mapM[$i][$j] != $mapN[$x+$i][$y+$j]) {
                    $bool = false;
                }
            }
        }
        if ($bool == true) {
            echo "Yes\n";
            exit;
        }
    }
}

echo "No\n";