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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;

class CF2016FC
{
	static bool[] comChecked;
	static List<int>[] comList;

	static public void Main(string[] args)
	{
		int N, M;
		string[] vals = Console.ReadLine().Split(' ');
		N = int.Parse(vals[0]);
		M = int.Parse(vals[1]);

		comList = new List<int>[N+1];
		for(int i=1; i<=N; i++)
		{
			comList[i] = new List<int>();
		}

		List<int>[] talkList = new List<int>[M+1];
		for(int i=1; i<=M; i++)
		{
			talkList[i] = new List<int>();
		}

		int K, L;
		for(int i=1; i<=N; i++)
		{
			vals = Console.ReadLine().Split(' ');
			K = int.Parse(vals[0]);
			for(int j=1; j<=K; j++)
			{
				L = int.Parse(vals[j]);
				foreach(int k in talkList[L])
				{
					comList[k].Add(i);
					comList[i].Add(k);
				}
				talkList[L].Add(i);
			}

		}
		
		comChecked = new bool[N+1];
		dfs(1);
		bool ans = true;
		for(int i=1; i<=N; i++)
		{
			if(comChecked[i] == false)
			{
				ans = false;
				break;
			}
		}

		if(ans)
			Console.WriteLine("YES");
		else
			Console.WriteLine("NO");
	}

	static void dfs(int i)
	{
		if(comChecked[i] == true)
			return;

		comChecked[i] = true;
		foreach(int j in comList[i])
		{
			dfs(j);
		}
	}

}