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.io.BufferedReader

fun main(args: Array<String>) {
    /** comment in when you submit **/
    System.`in`.bufferedReader().use { println(getOutputString(it)) }

    /** delete below after your test **/
    //executeTest()
}

private fun getOutputString(reader: BufferedReader): String {
    val lines = reader.readLines()
    val m = lines.last()
    lines.subList(0, lines.lastIndex - 1).forEach {
        if (it.indexOf(m) >= 0) {
            return "Yes"
        }
    }
    return "No"
}

/** delete below after your test **/
private fun String.mustBe(expected: String): Unit {
    if (this !=  expected) throw Exception("\"$this\" must be \"$expected\"")

    println("ok")
}

private fun executeTest() {
    getOutputString("3 2\n#.#\n.#.\n#.#\n#.\n.#".toByteArray(Charsets.UTF_8).inputStream().bufferedReader()).mustBe("Yes")
    getOutputString("4 1\n....\n....\n....\n....\n#".toByteArray(Charsets.UTF_8).inputStream().bufferedReader()).mustBe("No")
}