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 Ruby (2.3.3) (judge verdict: Wrong Answer)

N, M = gets.chomp.split.map(&:to_i)
as = Array.new(N)
N.times do |i|
  as[i] = gets.chomp
end

bs = Array.new(M)
M.times do |i|
  bs[i] = gets.chomp
end
sameflag = false
N.times do |i|
  line = 0
  # sameflag = true
  if N - M < i
    # sameflag = false
    break
  end 
  M.times do |j|
    newline = as[i + j].index(bs[j])
    if j == 0 && newline != nil
      line = newline
    end
    if line == newline
      sameflag = true
    else
      sameflag = false
      break
    end
  end
end

puts sameflag ? "Yes" : "No"
# puts as  
# puts bs