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 Go (1.6) (judge verdict: Wrong Answer)

package main

import "fmt"

func main() {
	var n, m int
	fmt.Scan(&n, &m)
	a := make([]string, n)
	for i := range a {
		fmt.Scan(&a[i])
	}
	b := make([]string, m)
	for i := range b {
		fmt.Scan(&b[i])
	}
	var ok bool
	for i := 0; i < n; i++ {
		for j := 0; j < n; j++ {
			// スタート地点が点(i,j)となる
			ok = true
			for k := 0; k < m && i+k < n; k++ {
				for l := 0; l < m && j+l < n; l++ { // O(N^4)だが、1<=N,M<=50のため間に合う
					if a[i][j] != b[k][l] {
						ok = false
						break
					}
				}
				if !ok {
					break
				}
			}
			if ok {
				fmt.Println("Yes")
				return
			}
		}
	}
	fmt.Println("No")
}