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::str::FromStr;

fn get_one<T : FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    return s.trim().parse().ok().unwrap();
}

fn get_vec<T : FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    return s.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect();
}

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

    let mut im_n : Vec<Vec<char>> = Vec::new();
    for _i in 0..n {
        let l_n : Vec<char> = get_one::<String>().chars().collect();
        im_n.push(l_n);
    }
    let mut im_m : Vec<Vec<char>> = Vec::new();
    for _i in 0..m {
        let l_m : Vec<char> = get_one::<String>().chars().collect();
        im_m.push(l_m);
    }
    let mut ans = false;
    for i in 0..(n-m+1) {
        for j in 0..(n-m+1) {
            let mut is_matched = true;
            for k in 0..m {
                for l in 0..m {
                    if im_n[i+k][j+l] != im_m[k][l] {
                        is_matched = false;
                        break;
                    }
                }
                if !is_matched {break;}
            }
            if is_matched {
                ans = true;
                break;
            }
        }
        if ans {break;}
    }

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