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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program ABC054B
    implicit none
    character(50)::s
    integer(8)::N,M,i,j,k,l,conv
    integer(8)::mask_sum=0
    integer(8)::flg=0
    integer(8),dimension(50,50)::img,mask
    read(5,*)N,M

    do i=1,N
        read(5,*)s
        do j=1,N
            if(s(j:j)==".")then
                img(j,i)=1
            else
                img(j,i)=0
            end if
        end do
    end do

    do i=1,M
        read(5,*)s
        do j=1,M
            if(s(j:j)==".")then
                mask(j,i)=1
                mask_sum=mask_sum+1
            else
                mask(j,i)=0
            end if
        end do
    end do


    do i=0,N-M
        do j=0,N-M
            conv=0
            do k=1,M
                do l=1,M
                    if(mask(l,k)==img(l+j,k+i))conv=conv+1
                end do
            end do
            if(conv==M*M)then
                flg=1
                exit
            end if
        end do
        if(flg==1)exit
    end do

    if(flg==1)then
        print'(A)',"Yes"
    else
        print'(A)',"No"
    end if
end program ABC054B