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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int main() {
  int square_a_line, square_b_line, i, j, k, l, flag;
  scanf("%d %d", &square_a_line, &square_b_line);
  char array[square_a_line];
  int square_a[square_a_line][square_a_line], square_b[square_b_line][square_b_line];
  for(i = 0; i < square_a_line; i++) {
    scanf("%s", array);
    for(j = 0; j < square_a_line; j++) {
      square_a[i][j] = (array[j] == '#')? 0 : 1;
    }
  }
  for(i = 0; i < square_b_line; i++) {
    scanf("%s", array);
    for(j = 0; j < square_b_line; j++) {
      square_b[i][j] = (array[j] == '#')? 0 : 1;
    }
  }
  for(i = 0; i <= square_a_line - square_b_line; i++) {
    if(flag == square_b_line * square_b_line) {
      break;
    }
    for(j = 0; j <= square_a_line - square_b_line; j++) {
      if(flag == square_b_line * square_b_line) {
        break;
      }
      flag = 0;
      for(k = 0; k < square_b_line; k++) {
        for(l = 0; l < square_b_line; l++) {
          if(square_a[i+k][j+l] == square_b[k][l]) {
            flag++;
          } else {
            break;
          }
        }
      }
    }
  }
  if(flag == square_b_line * square_b_line) {
    printf("Yes\n");
  } else {
    printf("No\n");
  }
  printf("%d\n", flag);
  return 0;
}