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 mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    let v: Vec<i32> = s
        .trim()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect();
    let n = v[0];
    let m = v[1];

    let mut a: Vec<Vec<char>> = Vec::new();
    for _i in 0..n {
        s = String::new();
        std::io::stdin().read_line(&mut s).ok();
        a.push(s.trim().chars().collect::<Vec<char>>());
    }
    let mut b: Vec<Vec<char>> = Vec::new();
    for _i in 0..m {
        s = String::new();
        std::io::stdin().read_line(&mut s).ok();
        b.push(s.trim().chars().collect::<Vec<char>>());
    }

    let mut c = false;
    'outer: for y in 0..n - m + 1 {
        for x in 0..n - m + 1 {
            c = diff(&a, &b, x, y, m);
            if c {
                break 'outer;
            }
        }
    }

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

fn diff(a: &Vec<Vec<char>>, b: &Vec<Vec<char>>, x: i32, y: i32, m: i32) -> bool {
    for j in 0..m {
        for i in 0..m {
            if a[(x + i) as usize][(y + j) as usize] != b[i as usize][j as usize] {
                return false;
            }
        }
    }
    true
}