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: Runtime Error)

#include <stdio.h>
#include <stdlib.h>

int main() {
  int N, M;
  scanf("%d %d%*c", &N, &M);
  int i, j;
  int** A, **B;
  A = (int**)malloc(sizeof(int) * N);
  for (i = 0; i < N; i++)
    A[i] = (int*)malloc(sizeof(int) * N);
  B = (int**)malloc(sizeof(int) * M);
  for (i = 0; i < M; i++)
    B[i] = (int*)malloc(sizeof(int) * M);
  char c;
  for (i = 0; i < N; i++) {
    for (j = 0; j < N; j++) {
      scanf("%c", &c);
      if (c == '.')
        A[i][j] = 0;
      else
        A[i][j] = 1;
    }
    scanf("%*c");
  }
  for (i = 0; i < M; i++) {
    for (j = 0; j < M; j++) {
      scanf("%c", &c);
      if (c == '.')
        B[i][j] = 0;
      else
        B[i][j] = 1;
    }
    scanf("%*c");
  }
  int k, l;
  int success;
  for (i = 0; i <= N - M; i++) {
    for (j = 0; j <= N - M; j++) {
      success = 1;
      for (k = 0; k < M; k++) {
        for (l = 0; l < M; l++) {
          if (A[i + k][j + l] != B[k][l]) {
            success = 0;
            break;
          }
          if (!success) break;
        }
      }
      if (success) break;
    }
    if (success) break;
  }
  if (success) printf("Yes\n");
  else printf("No\n");
  for (i = 0; i < N; i++)
    free(A[i]);
  for (i = 0; i < M; i++)
    free(B[i]);
  free(A);
  free(B);
  return 0;
}