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)

'use strict';

const input = require('fs').readFileSync('/dev/stdin', 'utf8').trim().split('\n');
const NM = input[0].split(' ').map(Number);
const N = NM[0];
const M = NM[1];

const As = input.slice(1, N + 1);
const Bs = input.slice(N + 1, N + M + 1);

for(let ax = 0; ax < N - M + 1; ax++) {
    for(let ay = 0; ay < N - M + 1; ay++) {
		let isMatch　= true
      	nextsearch:
        for(let bx = 0; bx < M; bx++){
            for(let by = 0; by < M; by++){
              	if(As[ax + bx][ay + by] != Bs[bx][by]){
                	isMatch = false;
                  	break nextsearch;
                }
            }
        }
        if(isMatch){
        	console.log("Yes")
          	return;
        }
    }
}
console.log('No');