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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Control.Monad( replicateM)
import Data.List( transpose)
main = do
    [n_, m_] <- return . map read . words =<< getLine
    alines_ <- replicateM n_ getLine
    blines_ <- replicateM m_ getLine
    let
	trimC n als = map (drop n) als
	trimR n als = drop n als
	trimTop [bl] = [bl]
	trimTop thru@(bl:bls)
	  | all ('.'==) bl = trimTop bls
	  | otherwise	    = thru
	trimBottom bls = reverse . trimTop $ reverse bls
	trimLR = transpose . trimBottom . trimTop . transpose 
	cleanse = trimLR . trimBottom . trimTop
	blines'@(b':_) = cleanse blines_
	mr = length blines'
	mc = length b'
	trims = [trimR tr.trimC tc$alines_| tc<-[0..n_-mc], tr<-[0..n_-mr]] 
    putStr $ if	any (blines'===) trims
	then "Yes"
	else "No"
      where
	bls === trim = let
	    (b,t) = unzip $ zip bls trim
	  in
	    b==t