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.*;
import static java.lang.Math.*;
import static java.util.Arrays.*;

public class CF {

    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int m = in.nextInt();
        int n = in.nextInt();
        Set<Integer> set = new HashSet<>();
        for (int i = 0; i < m; i++) {
            int a = in.nextInt();
            for (int j = 0; j < a; j++) {
                set.add(in.nextInt());
            }
        }
        if (set.size()==n){
            out.println("YES");
        }else{
            out.println("NO");
        }
        out.close();
    }

    static class FastScanner {

        private BufferedReader in;
        private String[] line;
        private int index;
        private int size;

        public FastScanner(InputStream in) throws IOException {
            this.in = new BufferedReader(new InputStreamReader(in));
            init();
        }

        public FastScanner(String file) throws FileNotFoundException {
            this.in = new BufferedReader(new FileReader(file));
        }

        private void init() throws IOException {
            line = in.readLine().split(" ");
            index = 0;
            size = line.length;
        }

        public int nextInt() throws IOException {
            if (index == size) {
                init();
            }
            return Integer.parseInt(line[index++]);
        }

        public long nextLong() throws IOException {
            if (index == size) {
                init();
            }
            return Long.parseLong(line[index++]);
        }

        public float nextFloat() throws IOException {
            if (index == size) {
                init();
            }
            return Float.parseFloat(line[index++]);
        }

        public double nextDouble() throws IOException {
            if (index == size) {
                init();
            }
            return Double.parseDouble(line[index++]);
        }

        public String next() throws IOException {
            if (index == size) {
                init();
            }
            return line[index++];
        }

        public String nextLine() throws IOException {
            if (index == size) {
                init();
            }
            StringBuilder sb = new StringBuilder();
            for (int i = index; i < size; i++) {
                sb.append(line[i]).append(" ");
            }
            return sb.toString();
        }

        private int[] nextIntArray(int n) throws IOException {
            int[] tab = new int[n];
            for (int i = 0; i < tab.length; i++) {
                tab[i] = nextInt();
            }
            return tab;
        }

        private double[] nextDoubleArray(int n) throws IOException {
            double[] tab = new double[n];
            for (int i = 0; i < tab.length; i++) {
                tab[i] = nextDouble();
            }
            return tab;
        }

    }

}
