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::io;

fn is_match(a: &Vec<String>, b: &Vec<String>, bx: usize, by: usize) -> bool {
    let m = b.len();
    for x in 0..m {
        for y in 0..m {
            if a[y + by].chars().nth(x + bx) != b[y].chars().nth(x) {
                return false;
            }
        }
    }
    true
}

fn solve(a: &Vec<String>, b: &Vec<String>) -> bool {
    let n = a.len();
    let m = b.len();
    for y in 0..(n-m+1) {
        for x in 0..(n-m+1) {
            if is_match(a, b, x, y) {
                return true
            }
        }
    }
    false
}

fn main() {
    let stdin = io::stdin();
    let input = &mut String::new();
    stdin.read_line(input);
    let mut iter = input.split_whitespace();
    let n = iter.next().unwrap().parse::<i32>().unwrap();
    let m = iter.next().unwrap().parse::<i32>().unwrap();
    let mut a = Vec::new();
    let mut b = Vec::new();
    for _ in 0..n {
        let input = &mut String::new();
        stdin.read_line(input);
        a.push(input.to_string());
    }
    for _ in 0..m {
        let input = &mut String::new();
        stdin.read_line(input);
        b.push(input.to_string());
    }
    let answer = if solve(&a, &b) { "Yes" } else { "No" };
    println!("{}", answer);
}