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 Python (3.8.2) (judge verdict: Wrong Answer)

from typing import List


def first_indexes(string: str, pattern: str) -> List[int]:
    indexes = []
    i = 0
    while i <= len(string) - len(pattern):
        index = string.find(pattern, i)
        if index != -1:
            indexes.append(index)
            i = index
        else:
            return indexes
        i += 1

    return indexes


def answer(n: int, m: int, a: List[str], b: List[str]) -> str:
    str_b = ''.join(b)
    for i in range(n - m):
        str_a = ''.join([line[i:i + m] for line in a])
        if str_b in str_a:
            bools = list(index % m == 0 for index in first_indexes(str_a, str_b))
            if any(bools):
                return 'Yes'

    return 'No'


def main():
    n, m = map(int, input().split())
    a = [input() for _ in range(n)]
    b = [input() for _ in range(m)]
    print(answer(n, m, a, b))


if __name__ == '__main__':
    main()