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.
/*
     * Code Author: Akshay Miterani
     * DA-IICT
     */
    import java.io.*;
    import java.util.*;
     
     
    public class ContestMode1 {
     
    	static double eps=(double)1e-6;
    	static long mod=(int)1e9+7;
    	public static void main(String args[]){
    		InputReader in = new InputReader(System.in);
    		OutputStream outputStream = System.out;
    		PrintWriter out = new PrintWriter(outputStream);
    		//----------My Code Starts Here----------
	    	int n=in.nextInt();
	    	int m=in.nextInt();
	    	boolean v[]=new boolean[m+1];
	    	for(int i=0;i<n;i++){
	    		int x=in.nextInt();
	    		for(int j=0;j<x;j++){
	    			int b=in.nextInt();
	    			v[b]=true;
	    		}
	    	}
	    	boolean f=true;
	    	for(int i=1;i<=m;i++){
	    		if(!v[i])
	    			f=false;
	    	}
	    	if(f){
	    		out.println("YES");
	    	}
	    	else{
	    		out.println("NO");
	    	}
    		out.close();
    		//---------------The End------------------
    	}
    	static long gcd(long x, long y)
        {
            long r=0, a, b;
            a = (x > y) ? x : y; // a is greater number
            b = (x < y) ? x : y; // b is smaller number
            r = b;
            while(a % b != 0)
            {
                r = a % b;
                a = b;
                b = r;
            }
            return r;
        }
    	static class Pair implements Comparable<Pair>{
    		long x;
    		long y;
    		int i;
    		Pair(long xx,long yy){
    			x=xx;
    			y=yy;
    		}
    		@Override
    		public int compareTo(Pair o) {
    			if(this.y==o.y)
					return Long.compare((this.x),(o.x));
				else
					return Long.compare((this.y),(o.y));
    		}
    	}
    	
    	static class InputReader {
    	    public BufferedReader reader;
    	    public StringTokenizer tokenizer;
     
    	    public InputReader(InputStream inputstream) {
    	      reader = new BufferedReader(new InputStreamReader(inputstream));
    	      tokenizer = null;
    	    }
    	    
    	    public String nextLine(){
    	    	String fullLine=null;
    	    	while (tokenizer == null || !tokenizer.hasMoreTokens()) {
    	            try {
    	              fullLine=reader.readLine();
    	            } catch (IOException e) {
    	              throw new RuntimeException(e);
    	            }
    	            return fullLine;
    	          }
    	          return fullLine;
    	    }
    		public String next() {
    	      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
    	        try {
    	          tokenizer = new StringTokenizer(reader.readLine());
    	        } catch (IOException e) {
    	          throw new RuntimeException(e);
    	        }
    	      }
    	      return tokenizer.nextToken();
    	    }
    		public long nextLong() {
    		      return Long.parseLong(next());
    		    }
    	    public int nextInt() {
    	      return Integer.parseInt(next());
    	    }
    	  }
    } 