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 JavaScript (node.js v5.12) (judge verdict: Accepted)


function Main(arg) {

  var n = arg.split("\n")[0].split(" ")[0] - 0;
  var m = arg.split("\n")[0].split(" ")[1] - 0;

  var A = new Array(n);
  var B = new Array(m);

  for (var i = 0; i < n; i++){
    A[i] = arg.split("\n")[i + 1].split("");
  }
  for (var i = 0; i < m; i++){
    B[i] = arg.split("\n")[n + 1 + i].split("");
  }
  
  for (var i = 0; i <= n - m; i++){
    for (var j = 0; j <= n - m; j++){
      var cnt = 0;
      for (var k = 0; k < m; k++){
        for (var l = 0; l < m; l++){
          if (A[i+k][j+l] == B[k][l]) cnt++;
        }
      }
      if (cnt == m * m) {
        console.log("Yes");
        return;
      }
    }
  }
  console.log("No");
  return;
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));