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: Accepted)

fn main() {
    let v = read_vec::<usize>();
    let n = v[0];
    let m = v[1];

    let mut im = vec![vec![false; n]; n];
    for i in 0..n {
        let line = read::<String>().chars().collect::<Vec<_>>();
        for j in 0..n {
            if line[j] == '#' {
                im[i][j] = true;
            }
        }
    }

    let mut tmp = vec![vec![false; m]; m];
    for i in 0..m {
        let line = read::<String>().chars().collect::<Vec<_>>();
        for j in 0..m {
            if line[j] == '#' {
                tmp[i][j] = true;
            }
        }
    }

    fn check(im: &Vec<Vec<bool>>, t: &Vec<Vec<bool>>, i: usize, j: usize, m: usize) -> bool {
        for x in 0..m {
            for y in 0..m {
                if t[x][y] != im[i + x][j + y] {
                    return false;
                }
            }
        }
        true
    }

    for i in 0..n - m + 1 {
        for j in 0..n - m + 1 {
            if check(&im, &tmp, i, j, m) {
                println!("Yes");
                return;
            }
        }
    }
    println!("No");
}

#[allow(dead_code)]
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}
#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}
#[allow(dead_code)]
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}
#[allow(dead_code)]
fn yn(result: bool) {
    if result {
        println!("Yes");
    } else {
        println!("No");
    }
}