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 (2.7.1) (judge verdict: Accepted)

class Problem
  attr_accessor :a, :b, :n, :m, :h, :w, :x, :y, :s ,:t

  def initialize
    @n,@m = gets.to_s.split.map{ |v| v.to_i }
    @a = Array.new(n){ gets.chomp }
    @b = Array.new(m){ gets.chomp }
  end

  def solve
    0.upto(n-m) do |y|
      0.upto(n-m) do |x|
        return true if match(y,x)
      end
    end
    false
  end

  def match(oy,ox)
    m.times do |y|
      m.times do |x|
        return false if b[y][x] != a[oy+y][ox+x]
      end
    end
    true
  end

  def show(ans)
    puts ans ? "Yes" : "No"
  end
end

Problem.new.instance_eval do
  show(solve)
end