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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;

/**
 * 
 * @author Code Forces.  Solution by: L.Azuaje.
 *
 * Problem: 615A Main.
 *
 * Used at Codeforces:  #338 Div-2 .
 *
 */

public class Main {

	public static void main(String[] args) throws IOException {
		MyScanner scanner = new MyScanner();
		PrintStream out = System.out;

        int[] data = scanner.nextIntArray();
        int buttons = data[0];
        int size = data[1];
        Integer[] elements;

        Set<Integer> set = new HashSet<Integer>();

        for (int i = 0; i < buttons; i++) {
            elements = scanner.nextIntegerArray();

            for (int j = 1; j < elements.length; j++) {
                set.add(elements[j]);
            }

        }

        String string = set.size() == size ? "YES" : "NO";

		out.println(string);

		scanner.close();
		out.close();
	}

	// -----------MyScanner class for faster input----------
	public static class MyScanner {
		BufferedReader reader;

		public MyScanner() {
			this.reader = new BufferedReader(new InputStreamReader(System.in));
		}

		public void close() throws IOException {
			this.reader.close();
		}

		int nextInt() {
			return Integer.parseInt(this.next());
		}

		long nextLong() {
			return Long.parseLong(this.next());
		}

		double nextDouble() {
			return Double.parseDouble(this.next());
		}

		String next() {
			String str = "";
			try {
				str = this.reader.readLine().trim();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

		String[] nextStringArray() {
			String[] str = null;
			try {
				str = this.reader.readLine().trim().split(" ");
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

		int[] nextIntArray() {
			String[] data  = nextStringArray();
			int[] a  = new int[data.length];

			for (int i = 0; i < a.length; i++) {
				a[i] = Integer.parseInt(data[i]);
			}

			return a;
		}

		Integer[] nextIntegerArray() {
			String[] data  = nextStringArray();
			Integer[] a  = new Integer[data.length];

			for (int i = 0; i < a.length; i++) {
				a[i] = Integer.parseInt(data[i]);
			}

			return a;
		}

		long[] nextLongArray() {
			String[] data  = nextStringArray();
			long[] a  = new long[data.length];

			for (int i = 0; i < a.length; i++) {
				a[i] = Long.parseLong(data[i]);
			}

			return a;
		}
	}
}

