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 (3.4.3) (judge verdict: Runtime Error)

# -*- coding:utf-8 -*-

def solve():
    N, M = list(map(int, input().split()))
    A = []
    B = []

    for i in range(N):
        A.append(list(input()))
    for i in range(M):
        B.append(list(input()))
    
    # 左上から順に走査する
    for i in range(N-M+1):
        for j in range(N-M+1):
            if A[i][j] == B[0][0]:
                is_contained = True
                for k in range(i, i+M):
                    for l in range(j, j+M):
                        if A[k][l] != B[k][l]:
                            is_contained = False
                            break
                    if not is_contained: break
                if is_contained:
                    print("Yes")
                    return
    print("No")


if __name__ == "__main__":
    solve()