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
import qualified Data.List as L

main :: IO ()
main = do
  [n, m] <- getNums <$> getLine
  as <- replicateM n getLine
  bs <- replicateM m getLine
  let msg = if (solve as bs (n, m)) then "Yes" else "No"
  putStrLn msg
  
getNums :: String -> [Int]
getNums = map read . words

solve :: [String] -> [String] -> (Int, Int) -> Bool
solve as bs (n, m) = _solve as bs 0 0
  where
    _solve :: [String] -> [String] -> Int -> Int -> Bool
    _solve as bs x y = if matrixEquals ass bs
                       then True
                       else if x + 1 > n
                            then if y + 1 > n
                                 then False
                                 else _solve as bs 0 (y+1)
                            else _solve as bs (x+1) y
                       where
                         ass = getSubMatrix m x y (n, m) as     

getSubMatrix :: Int -> Int -> Int -> (Int, Int) ->  [String] -> [String]
getSubMatrix size x y (n, m)as =
  map _getSubMatrix ass
  where
    ass = if size + x > n || size + y > n
          then ["a"]
          else (take size . drop x) as
    _getSubMatrix ls
      | null ls = "a"
      | otherwise = (take size . drop (m - size)) ls

matrixEquals :: [String] -> [String] -> Bool
matrixEquals as bs = all (\(a, b) -> a == b) $ zip as bs