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.math.*;
import java.util.*;
import java.util.stream.*;

@SuppressWarnings("unchecked")
public class P615A {

  public void run() throws Exception {
    int n = nextInt();
    int m = nextInt();

    BitSet lamps = new BitSet(m);
    while ((n--) > 0) {
      for (int k = nextInt(); k > 0; k--) {
        lamps.set(nextInt());
      }
    }

    println((lamps.cardinality() == m) ? "YES" : "NO");
  }

  public static void main(String... args) throws Exception {
    br = new BufferedReader(new InputStreamReader(System.in));
    pw = new PrintWriter(new BufferedOutputStream(System.out));
    new P615A().run();
    br.close();
    pw.close();
    System.err.println("\n[Time : " + (System.currentTimeMillis() - startTime) + " ms]");
  }

  static long startTime = System.currentTimeMillis();
  static BufferedReader br;
  static PrintWriter pw;
  StringTokenizer stok;

  String nextToken() throws IOException {
    while (stok == null || !stok.hasMoreTokens()) {
      String s = br.readLine();
      if (s == null) { return null; }
      stok = new StringTokenizer(s);
    }
    return stok.nextToken();
  }

  void print(byte b) { print("" + b); }
  void print(int i) { print("" + i); }
  void print(long l) { print("" + l); }
  void print(double d) { print("" + d); }
  void print(char c) { print("" + c); }
  void print(Object o) {
    if (o instanceof int[]) { print(Arrays.toString((int [])o));
    } else if (o instanceof long[]) { print(Arrays.toString((long [])o));
    } else if (o instanceof char[]) { print(Arrays.toString((char [])o));
    } else if (o instanceof byte[]) { print(Arrays.toString((byte [])o));
    } else if (o instanceof short[]) { print(Arrays.toString((short [])o));
    } else if (o instanceof boolean[]) { print(Arrays.toString((boolean [])o));
    } else if (o instanceof float[]) { print(Arrays.toString((float [])o));
    } else if (o instanceof double[]) { print(Arrays.toString((double [])o));
    } else if (o instanceof Object[]) { print(Arrays.toString((Object [])o));
    } else { print("" + o); }
  }
  void print(String s) { pw.print(s); }
  void println() { println(""); }
  void println(byte b) { println("" + b); }
  void println(int i) { println("" + i); }
  void println(long l) { println("" + l); }
  void println(double d) { println("" + d); }
  void println(char c) { println("" + c); }
  void println(Object o) { print(o); println(); }
  void println(String s) { pw.println(s); }
  int nextInt() throws IOException { return Integer.parseInt(nextToken()); }
  long nextLong() throws IOException { return Long.parseLong(nextToken()); }
  double nextDouble() throws IOException { return Double.parseDouble(nextToken()); }
  char nextChar() throws IOException { return (char) (br.read()); }
  String next() throws IOException { return nextToken(); }
  String nextLine() throws IOException { return br.readLine(); }
  int [] readInt(int size) throws IOException {
    int [] array = new int [size];
    for (int i = 0; i < size; i++) { array[i] = nextInt(); }
    return array;
  }
  long [] readLong(int size) throws IOException {
    long [] array = new long [size];
    for (int i = 0; i < size; i++) { array[i] = nextLong(); }
    return array;
  }
  double [] readDouble(int size) throws IOException {
    double [] array = new double [size];
    for (int i = 0; i < size; i++) { array[i] = nextDouble(); }
    return array;
  }
  String [] readLines(int size) throws IOException {
    String [] array = new String [size];
    for (int i = 0; i < size; i++) { array[i] = nextLine(); }
    return array;
  }
}