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: Accepted)

package main

import (
	"bufio"
	"fmt"
	"io"
	"os"
	"strconv"
)

var nextString func() string

func init() {
	nextString = newReadString(os.Stdin)
}

func main() {
	N := nextInt()
	M := nextInt()
	A := make([]string, N)
	for i := 0; i < N; i++ {
		A[i] = nextString()
	}
	B := make([]string, M)
	for i := 0; i < M; i++ {
		B[i] = nextString()
	}
	ans := "No"

	for Ni := 0; Ni < N; Ni++ {
		for Nj := 0; Nj < N; Nj++ {
			if judge(Ni, Nj, N, M, A, B) {
				ans = "Yes"
				break
			}
			if ans == "Yes" {
				break
			}
		}
	}
	fmt.Println(ans)
}

func judge(Ni, Nj, N, M int, A, B []string) (result bool) {
	for i := 0; i < M; i++ {
		for j := 0; j < M; j++ {
			if Ni+i >= N || Nj+j >= N {
				return
			}
			if B[i][j] != A[Ni+i][Nj+j] {
				return
			}
		}
	}
	return true
}

func nextInt() (result int) {
	result, _ = strconv.Atoi(nextString())
	return
}

func newReadString(ior io.Reader) func() string {
	r := bufio.NewScanner(ior)
	r.Buffer(make([]byte, 1024), int(1e+11))
	r.Split(bufio.ScanWords)

	return func() string {
		if !r.Scan() {
		}
		return r.Text()
	}
}