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: Accepted)

#[allow(dead_code)]

pub struct Scanner {
    idx: usize, 
    buf: Vec<String>,
}

impl Scanner {
    pub fn new<T: std::io::Read>(inf: &mut T) -> Scanner {
        Self {
            idx:0,
            buf: {
                let mut s = String::new();
                inf.read_to_string(&mut s).expect("I/O error");
                s.split_whitespace().map(|x| x.to_owned()).collect()
            },
        }
    }

    pub fn read<T: std::str::FromStr> (&mut self) -> T 
    where
        <T as std::str::FromStr>::Err: std::fmt::Debug,
    {
        if self.empty() {
            panic!("reached the end of input")
        }
        let ret = self.buf[self.idx].parse::<T>().expect("parse error");
        self.idx += 1;
        return ret;
    }

    pub fn empty(&self) -> bool {
        return self.idx >= self.buf.len();
    }
}

fn main() {
    let mut sc = Scanner::new(&mut std::io::stdin());
    let n: usize = sc.read();
    let m: usize = sc.read();
    let a: Vec<Vec<char>> = (0..n).map(|_| sc.read::<String>().chars().collect()).collect();
    let b: Vec<Vec<char>> = (0..m).map(|_| sc.read::<String>().chars().collect()).collect();

    let mut ans = false;

    for i in 0..n {
        for j in 0..n {
            let mut cnt = 0;
            for ii in 0..m {
                for jj in 0..m {
                    if i + ii >= n || j + jj >= n {
                        continue;
                    }
                    if a[i + ii][j + jj] == b[ii][jj] {
                        cnt += 1;
                    }
                }
            }
            if cnt >= m * m {
                ans = true;
            }
        }
    }


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