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: Accepted)

import Data.Bool
import qualified Data.Set as S
import Control.Monad

main = do
 [n,m] <- map read . words <$> getLine
 ta <- concat <$> replicateM n getLine
 tb <- concat <$> replicateM m getLine
 let pa = map fst $ filter ((=='#') . snd) $ zip [(h,w) | h<-[0..n-1], w<-[0..n-1]] ta
 let pb = map fst $ filter ((=='#') . snd) $ zip [(h,w) | h<-[0..m-1], w<-[0..m-1]] tb
 let sa = S.fromDistinctAscList pa
 let sb = S.fromDistinctAscList pb
 let d = n - m
 putStrLn $ bool "No" "Yes" (templateMatch d sa sb)

templateMatch d sa sb = any (match sa sb) [(dh,dw) | dh<-[0..d], dw<-[0..d]]

match sa sb (dh,dw) = S.mapMonotonic (move dh dw) sb `S.isSubsetOf` sa

move dh dw (h,w) = (h+dh, w+dw)