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)

use std::vec::Vec;

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()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn read_touple<T: std::str::FromStr + Copy>() -> (T, T) {
    let v: Vec<T> = read_vec();
    assert_eq!(v.len(), 2);
    (v[0], v[1])
}

fn main() {
    let (n, m) = read_touple::<usize>();
    let mut a = vec![];
    let mut b = vec![];
    for _ in 0..n {
        let t: Vec<char> = read::<String>().chars().collect();
        a.push(t);
    }

    for _ in 0..m {
        let t: Vec<char> = read::<String>().chars().collect();
        b.push(t);
    }

    for i in 0..n - m + 1 {
        for j in 0..n - m + 1 {
            if check(&a, &b, i, j) {
                println!("Yes");
                return;
            }
        }
    }

    println!("No");
}

fn check(a: &Vec<Vec<char>>, b: &Vec<Vec<char>>, i: usize, j: usize) -> bool {
    let m = b.len();

    for k in 0..m {
        for l in 0..m {
            if a[i + k][j + l] != b[k][l] {
                return false;
            }
        }
    }

    true
}