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 PyPy3 (2.4.0) (judge verdict: Runtime Error)

def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]

from collections import defaultdict, deque, Counter
from sys import exit
import heapq
import math
import copy
from bisect import bisect_left, bisect_right

import sys
sys.setrecursionlimit(1000000000)

def dfs(idx, end, value, cost, g):
    if idx == end:
        if cost == 0:
            return

        if value not in g:
            g[value] = cost
        else:
            g[value] = min(g[value], cost)

        return

    a, b, c = table[idx]
    dfs(idx + 1, end, value + b * Ma - a * Mb, cost + c, g)
    dfs(idx + 1, end, value, cost, g)

N, Ma, Mb = map(int, input().split())
table = [tuple(map(int, input().split())) for i in range(N)]

g1, g2 = dict(), dict()
dfs(0, N // 2, 0, 0, g1)
dfs(N // 2, N, 0, 0, g2)

inf = 100*40 + 1
ans = inf

if 0 in g1:
    ans = min(ans, g1[0])
if 0 in g2:
    ans = min(ans, g2[0])

for v1, c1 in g1.items():
    if -v1 in g2:
        tmp = c1 + g2[-v1]
        ans = min(ans, tmp)

if ans < inf:
    print(ans)
else:
    print(-1)