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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.util.*

fun main(args: Array<String>) {
    val sc = Scanner(System.`in`)
    val n = sc.next().toInt()
    val m = sc.next().toInt()
    val aList = (0 until n).map { sc.next() }
    val bList = (0 until m).map { sc.next() }
    println(problem54b(n, m, aList, bList))
}

fun problem54b(n: Int, m: Int, aList:List<String>, bList:List<String>): String {
    val bListY = bList.size
    val bListX = bList[0].length
    aList.forEachIndexed { i, s ->
        if (i + bListY - 1 > aList.size - 1) return@forEachIndexed
        (0 until aList[0].length).forEach { j ->
            if (j + bListX > aList[0].length - 1) return@forEach
            val subSquare = aList.drop(i).map { it.substring(j, j + bListX) }.take(bListY)
            if (subSquare == bList) return "Yes"
        }
    }
    return "No"
}