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)

n,m = map(int, raw_input().split())
n_list = [] #row major format
m_list = []
for i in range(0, n):
	n_list.append(raw_input())

for x in range(0, m):
	m_list.append(raw_input())

def match_first_rows(n_start):
	result = (-1,-1)
	first_m = m_list[0] # first row
	for x in range(n_start, n):
		n_row = n_list[x]
		if first_m in n_row: # substring matching of first m_row
			j = n_row.index(first_m)
			return (x, j)
	return (-1,-1) #return -1,-1 if none found

# given the leftmost corner of matching in matrix n, start matching each row to see if there is a potential match
# only guranteed first row match
def begin_matching(i,j):
	nx_start = i
	ny_start = j
	for x in range(0,m):
		n_row_string = n_list[nx_start+x]
		n_string = n_row_string[j:j+m] # align window
		m_string = m_list[x]
		if n_string!=m_string:
			return False
	return True

def find_m():

	found_m = False
	counter = 0
	while(counter<n and not(found_m)):

		i,j = match_first_rows(counter)
		if i==-1: 
			#goes through entirety, not returning things at all
			print("No")
			found_m = True
		# found a potential starting point
		else:
			result = begin_matching(i,j)
			if result:
				print("Yes")
				found_m = True
			else:
				#do it again, but one row lower
				counter +=1 

find_m()