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 io::*;
use std::*;

const YES: &'static str = "Yes";
const NO: &'static str = "No";
fn solve(N: i64, M: i64, A: Vec<String>, B: Vec<String>) {
    let mut n = vec![vec![0; N as usize]; N as usize];
    let mut m = vec![vec!['#'; M as usize]; M as usize];

    let mut corner = ('#', '#', '#', '#');

    for i in 0..M as usize {
        for j in 0..M as usize {
            match B[i as usize].chars().nth(j as usize) {
                Some('.') => {
                    if i == 0 && j == 0 {
                        corner.0 = '.';
                    } else if i == 0 && j == M as usize - 1 {
                        corner.1 = '.';
                    } else if i == M as usize - 1 && j == 0 {
                        corner.2 = '.';
                    } else if i == M as usize - 10 && j == M as usize - 1 {
                        corner.3 = '.';
                    }
                    m[i][j] = '.'
                }
                Some('#') => m[i][j] = '#',
                _ => unreachable!(),
            }
        }
    }
    let n = (N - M) as usize;
    let ml = (M - 1) as usize;
    let mut start = 0;
    for i in 0..n + 1 {
        for j in 0..n + 1 {
            let c0 = A[i].chars().nth(j).unwrap();
            let c1 = A[i].chars().nth(j + ml).unwrap();
            let c2 = A[i + ml].chars().nth(j).unwrap();
            let c3 = A[i + ml].chars().nth(j + ml).unwrap();
            let mut ok = true;
            for k in 0..M as usize {
                for l in 0..M as usize {
                    let c = A[i + k].chars().nth(j + l).unwrap();
                    if c != m[k][l] {
                        ok = false;
                    }
                }
            }
            if ok {
                println!("{}", YES);
                return;
            }
        }
    }
    println!("{}", NO);
}

// Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
fn main() {
    let con = read_string();
    let mut scanner = Scanner::new(&con);
    let mut N: i64;
    N = scanner.next();
    let mut M: i64;
    M = scanner.next();
    let mut A: Vec<String> = vec![String::new(); (N) as usize];
    for i in 0..(N) as usize {
        A[i] = scanner.next();
    }
    let mut B: Vec<String> = vec![String::new(); (M) as usize];
    for i in 0..(M) as usize {
        B[i] = scanner.next();
    }
    // In order to avoid potential stack overflow, spawn a new thread.
    let stack_size = 104_857_600; // 100 MB
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(move || solve(N, M, A, B))
        .unwrap()
        .join()
        .unwrap();
}

pub mod io {
    use std;
    use std::str::FromStr;

    pub struct Scanner<'a> {
        iter: std::str::SplitWhitespace<'a>,
    }

    impl<'a> Scanner<'a> {
        pub fn new(s: &'a str) -> Scanner<'a> {
            Scanner {
                iter: s.split_whitespace(),
            }
        }

        pub fn next<T: FromStr>(&mut self) -> T {
            let s = self.iter.next().unwrap();
            if let Ok(v) = s.parse::<T>() {
                v
            } else {
                panic!("Parse error")
            }
        }

        pub fn next_vec_len<T: FromStr>(&mut self) -> Vec<T> {
            let n: usize = self.next();
            self.next_vec(n)
        }

        pub fn next_vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
            (0..n).map(|_| self.next()).collect()
        }
    }

    pub fn read_string() -> String {
        use std::io::Read;

        let mut s = String::new();
        std::io::stdin().read_to_string(&mut s).unwrap();
        s
    }

    pub fn read_line() -> String {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        s.trim_right().to_owned()
    }
}