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 (1.42.0) (judge verdict: Wrong Answer)

use proconio::{fastout, input};
#[allow(unused_mut)]
#[fastout]
fn main() {
    input! {
        n: usize, m: usize,
        a: [String; n],
        b: [String; m]
    }
    let a = a.iter().map(|s| s.chars().collect()).collect();
    let b = b.iter().map(|s| s.chars().collect()).collect();
    let mut res = false;
    let diff = n - m;
    for x in 0..diff {
        for y in 0..diff {
            if check(x, y, &a, &b) {
                res = true;
            }
        }
    }
    println!("{}", if res { "Yes" } else { "No" })
}

fn check(sx: usize, sy: usize, a: &Vec<Vec<char>>, b: &Vec<Vec<char>>) -> bool {
    let m = b.len();
    for x in sx..sx + m {
        for y in sy..sy + m {
            if a[y][x] != b[y - sy][x - sx] {
                return false;
            }
        }
    }
    true
}