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 OCaml (4.10.0) (judge verdict: Accepted)

(* unihernandez22
 * https://atcoder.jp/contests/abc054/tasks/abc054_b
 * implementation
 * *)

Scanf.scanf "%d %d\n" @@ fun n m ->
    let a = Array.init n @@ fun _ -> Scanf.scanf "%s\n" @@ fun s -> s in
    let b = Array.init m @@ fun _ -> Scanf.scanf "%s\n" @@ fun s -> s in

    let valid = ref true in
    let ans = ref "No\n" in
    for i = 0 to n-m do
        for j = 0 to n-m do
            valid := true;
            for y = 0 to m-1 do
                if String.sub a.(i+y) j m <> b.(y) then
                    valid := false;
            done;
            if !valid then
                ans := "Yes\n";
        done;
    done;
    print_string !ans;;