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 Rust (1.15.1) (judge verdict: Wrong Answer)

fn main() {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let v: Vec<usize> = s.trim().split_whitespace().map(|x| x.parse().unwrap()).collect();
    let mut a: Vec<Vec<char>> = Vec::new();
    let mut b: Vec<Vec<char>> = Vec::new();

    for _ in 0..v[0] {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        a.push(s.trim().chars().collect::<Vec<char>>());
    }
    for _ in 0..v[1] {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        b.push(s.trim().chars().collect::<Vec<char>>());
    }

    let mut z: bool = false;

    for i in 0..v[0]-v[1] {
        for j in 0..v[0]-v[1] {
            if a[i][j] == b[0][0] {
                z = true;
                for x in i..v[1] {
                    for y in j..v[1] {
                        if a[x][y] != b[x-i][y-j] {z = false; break;}
                    }
                    if !z {break;}
                }
            }
            if z {break;}
        }
    }

    println!("{}", if z {"Yes"} else {"No"});
}