Problem:
Score : 400 points

Problem Statement

On a planet far, far away, M languages are spoken. They are conveniently numbered 1 through M.

For CODE FESTIVAL 20XX held on this planet, N participants gathered from all over the planet.

The i-th (1≦i≦N) participant can speak K_i languages numbered L_{i,1}, L_{i,2}, ..., L_{i,{}K_i}.

Two participants A and B can communicate with each other if and only if one of the following conditions is satisfied:

There exists a language that both A and B can speak.

There exists a participant X that both A and B can communicate with.

Determine whether all N participants can communicate with all other participants.

Constraints

2≦N≦10^5

1≦M≦10^5

1≦K_i≦M

(The sum of all K_i)≦10^5

1≦L_{i,j}≦M

L_{i,1}, L_{i,2}, ..., L_{i,{}K_i} are pairwise distinct.

Partial Score

200 points will be awarded for passing the test set satisfying the following: N≦1000, M≦1000 and (The sum of all K_i)≦1000.

Additional 200 points will be awarded for passing the test set without additional constraints.

Input

The input is given from Standard Input in the following format:

N M
K_1 L_{1,1} L_{1,2} ... L_{1,{}K_1}
K_2 L_{2,1} L_{2,2} ... L_{2,{}K_2}
:
K_N L_{N,1} L_{N,2} ... L_{N,{}K_N}

Output

If all N participants can communicate with all other participants, print YES. Otherwise, print NO.

Sample Input 1

4 6
3 1 2 3
2 4 2
2 4 6
1 6

Sample Output 1

YES

Any two participants can communicate with each other, as follows:

Participants 1 and 2: both can speak language 2.

Participants 2 and 3: both can speak language 4.

Participants 1 and 3: both can communicate with participant 2.

Participants 3 and 4: both can speak language 6.

Participants 2 and 4: both can communicate with participant 3.

Participants 1 and 4: both can communicate with participant 2.

Note that there can be languages spoken by no participant.

Sample Input 2

4 4
2 1 2
2 1 2
1 3
2 4 3

Sample Output 2

NO

For example, participants 1 and 3 cannot communicate with each other.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

 
public class Main {
	static final long MOD1=1000000007;
	static final long MOD2=998244353;
	public static void main(String[] args) {
		PrintWriter out = new PrintWriter(System.out);
		InputReader sc=new InputReader(System.in);
		int N=sc.nextInt();
		int M=sc.nextInt();
		UnionFindTree unionFindTree=new UnionFindTree(M+N);
		for (int i = 0; i < N; i++) {
			int K=sc.nextInt();
			for (int j = 0; j < K; j++) {
				unionFindTree.union(i, N+(sc.nextInt()-1), 0);
			}
		}
		HashSet<Integer> hashSet=new HashSet<>();
		for (int i = 0; i < N; i++) {
			hashSet.add(unionFindTree.find(i));
		}
		if (hashSet.size()==1) {
			System.out.println("YES");
		}else {
			System.out.println("NO");
		}
	}
	static class UnionFindTree{
    	int[] par;
    	int[] rank;
    	int[] size;
    	int[] diff_weight;
    	int arraysize;
    	public UnionFindTree(int n) {
    		this.par=new int[n];
    		this.rank=new int[n];
    		this.size=new int[n];
    		this.diff_weight=new int[n];
    		arraysize=n;
    		for (int i = 0; i < arraysize; i++) {
				set(i);
			}
    	}
    	public void set(int i) {
    		par[i]=i;
    		rank[i]=0;
    		size[i]=1;
    		diff_weight[i]=0;
    	}
    	public void union(int x,int y,int w) {
    		w += weight(x); 
    		w -= weight(y);
    		int rootx=find(x);
    		int rooty=find(y);
    		if (rootx==rooty) {
				return;
			}
    		if (rank[rootx]>rank[rooty]) {
				par[rooty]=rootx;
				diff_weight[rooty] = w;
				size[rootx]+=size[rooty];
			}
    		else if (rank[rootx]<rank[rooty]) {
				par[rootx]=rooty;
				w=-w;
				diff_weight[rootx] = w;
				size[rooty]+=size[rootx];
			}
    		else {
    			par[rooty]=rootx;
    			diff_weight[rooty] = w;
    			rank[rootx]++;
				size[rootx]+=size[rooty];
			}
    	}
    	public int find(int x) {
    		if(par[x] == x) return x;
    		int r = find(par[x]);
    		diff_weight[x] += diff_weight[par[x]];
    		return par[x] = r;
    	}
    	public int weight(int x) {
    		find(x);
    		return diff_weight[x];
    	}
    	public int size(int i) {
            return size[find(i)];
        }
    	public int diff(int x, int y) {
    		return weight(y) - weight(x);
    	}
    	public boolean same(int x, int y) {
            return find(x) == find(y);
        }
    }
		static class InputReader { 
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;
		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}
 
		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}
 
		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}
 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
 
		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}
 
		public boolean hasNext() {
			skip();
			return hasNextByte();
		}
 
		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
 
		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public double nextDouble() {
			return Double.parseDouble(next());
		}
 
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
 
		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}
 
		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
}