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)

// ABC054 B - Template Matching
'use strict'

function Main(input) {
    const tmp = input.trim().split('\n');
    const NM = tmp[0].split(' ');
    const N = Number(NM[0])
    const M = Number(NM[1])
    const AB = tmp.splice(1);
    const A = AB.slice(0, N);
    const B = AB.slice(-M);
    // console.log(N, M, A, B);

    const joinB = B.join('');
    for (let y = 0; y < (N - M + 1); y++) {
        for (let x = 0; x < (N - M + 1); x++) {
            if (A[y][x] === joinB[0]) {
                // joinAを作る
                let joinA = '';
                for (let i = 0; i < M; i++) {
                    joinA += A[y + i].slice(x, x + M)
                }
                // joinAとjoinBが同じならYes
                if (joinA === joinB) {
                    console.log('Yes');
                    return;
                }
            }
        }
    }
    console.log('No');
    return;

}


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