Vasya wants to turn on Christmas lights consisting of m bulbs. Initially, all bulbs are turned off. There are n buttons, each of them is connected to some set of bulbs. Vasya can press any of these buttons. When the button is pressed, it turns on all the bulbs it's connected to. Can Vasya light up all the bulbs?

If Vasya presses the button such that some bulbs connected to it are already turned on, they do not change their state, i.e. remain turned on.

Input

The first line of the input contains integers n and m (1 ≤ n, m ≤ 100) — the number of buttons and the number of bulbs respectively. 

Each of the next n lines contains xi (0 ≤ xi ≤ m) — the number of bulbs that are turned on by the i-th button, and then xi numbers yij (1 ≤ yij ≤ m) — the numbers of these bulbs.

Output

If it's possible to turn on all m bulbs print "YES", otherwise print "NO".

Examples

Input

3 4
2 1 4
3 1 3 1
1 2


Output

YES


Input

3 3
1 1
1 2
1 1


Output

NO

Note

In the first sample you can press each button once and turn on all the bulbs. In the 2 sample it is impossible to turn on the 3-rd lamp.
import java.io.*;
import java.util.*;

public class cf338_a {
    private final boolean fileInput = false;
    private final String fileName = "";

    public void solve() throws IOException {
        int n = nextInt();
        int m = nextInt();
        int k = 0;
        int []a = new int[m];
        for (int i = 0; i < n; i++) {
            k = nextInt();
            for (int j = 0; j < k; j++) {
                a[nextInt() - 1]++;
            }
        }
        boolean can = true;
        for (int i = 0; i < m; i++) {
            if (a[i] == 0){
                can = false;
            }
        }
        if (can) {
            out.print("YES");
        } else {
            out.print("NO");
        }
    }

    public void run() throws IOException {
        try {
            if (fileInput) {
                br = new BufferedReader(new FileReader(new File(fileName + ".in")));
                out = new PrintWriter(fileName + ".out");
            } else {
                br = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            }
            solve();
            br.close();
            out.close();
        } catch (IOException e) {

        }

    }

    public static void main(String[] args) throws IOException {
        new cf338_a().run();
    }

    BufferedReader br;
    StringTokenizer in;
    PrintWriter out;

    public String nextToken() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            try {
                in = new StringTokenizer(br.readLine());
            } catch (IOException | NullPointerException e) {
                throw new IOException();
            }
        }
        return in.nextToken();
    }

    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public void log(String s) {
        System.out.print(s);
    }

    public void logln(String s) {
        System.out.println(s);
    }
}