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;
use std::io::Read;

fn main() {
    let mut stdin = io::stdin();
    let mut lines = String::new();
    let _ = stdin.read_to_string(&mut lines);
    let vec = lines.lines().collect::<Vec<&str>>();
    let firstline = vec[0].split(' ').collect::<Vec<&str>>();
    let n :usize = firstline[0].trim().parse().unwrap();
    let m :usize = firstline[1].trim().parse().unwrap();
    let mkono1 :u64 = (1 << m) - 1;
    let mut a :Vec<u64> = Vec::new();
    for i in 0..n {
        let mut thisline :u64 = 0;
        for (j, c) in vec[i+1].trim().chars().enumerate() {
            match c {
                '#' => {thisline = thisline + (1 << j);},
                _ => {},
            }
        }
        a.push(thisline);
    }
    let a = a;
    let mut b :Vec<u64> = Vec::new();
    for i in 0..m {
        let mut thisline :u64 = 0;
        for (j, c) in vec[i+n+1].trim().chars().enumerate() {
            match c {
                '#' => {thisline = thisline + (1 << j);},
                _ => {},
            }
        }
        b.push(thisline);
    }
    let b = b;
    'tate: for i in 0..(n-m+1) {
        'yoko: for j in 0..(n-m+1) {
            'chekku: for k in 0..m {
                let bline = b[k];
                let aline = (a[k+i] >> j) & mkono1;
                if aline ^ bline != 0 {continue 'yoko;}
            }
            println!("Yes");
            return;
        }
    }
    println!("No");
}