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 Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(defun split (str delim)
  (let ((res (make-array 1 :element-type 'string
                           :fill-pointer 0
                           :adjustable t)))
    (loop for i from 0 below (length str)
          with start = 0
          when (eq (char str i) delim)
          do (vector-push-extend (subseq str start i) res)
             (setf start (1+ i))
          finally (let ((tail (subseq str start)))
                    (when tail
                      (vector-push-extend tail res))))
    res))

(let* ((l (map 'vector #'parse-integer (split (read-line) #\ )))
       (a (aref l 0))
       (b (aref l 1))
       (w (- a (- a b)))
       (aimg (make-array `(,a ,a) :adjustable t))
       (bimg (make-array `(,b ,b) :adjustable t)))
  (dotimes (i a)
    (let ((line (read-line)))
      (dotimes (j a)
        (setf (aref aimg i j) (aref line j)))))
  (dotimes (i b)
    (let ((line (read-line)))
      (dotimes (j b)
        (setf (aref bimg i j) (aref line j)))))
  (if 
   (loop for y from 0 below w
         when (loop for x from 0 below w
                    for frag = 0
                    do (loop for j from 0 below b
                             do (incf frag
                                      (loop for i from 0 below b
                                            count (eq (aref aimg (+ x i) (+ y j))
                                                      (aref bimg i j)))))
                    when (= frag (* b b))
                    do (return t))
         return t)
   (format t "Yes~%")
   (format t "No~%")))