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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashSet;
import java.util.List;
import java.util.Set;

public class Main {
	final int _intMax = Integer.MAX_VALUE; //=2147483647>10^9
	final long _longMax = Long.MAX_VALUE; //=9223372036854775807L>10^18
	static boolean bElapsed = false;
	List<Node> list = new ArrayList<>();
	int n;
	int m;

	void solve() {
		int[] ia = readNums();
		n = ia[0];
		m = ia[1];
		for (int i=0; i<n+m; i++) {
			list.add(new Node());
		}
		for (int i=0; i<n; i++) {
			Node n1 = list.get(i);
			ia = readNums();
			for (int j=1; j<ia.length; j++) {
				int k = n+ia[j]-1;
				Node n2 = list.get(k);
				n1.link.add(k);
				n2.link.add(i);
			}
		}
		dfs(0);
		for (int i=0; i<n; i++) {
			Node n = list.get(i);
			if (!n.vt) {
				pln("NO");
				return;
			}
		}
		pln("YES");
	}
	void dfs(int i) {
		Node n = list.get(i);
		if (n.vt) return;
		n.vt = true;
		for (int l : n.link) {
			dfs(l);
		}
	}
	class Node {
		boolean vt;
		Set<Integer> link = new HashSet<>();
	}

	class UnionFind {
		int[] uf;
		public UnionFind(int n) {
			uf = new int[n];
			for (int i=0; i<n; i++) {
				uf[i] = i;
			}
		}
		public int root(int v) {
			if (uf[v] == v) return v;
			uf[v] = root(uf[v]);
			return uf[v];
		}
		public void merge(int u, int v) {
			u = root(u);
			v = root(v);
			if (u == v) return;
			uf[v] = u;
		}
		public boolean same(int u, int v) {
			return root(u) == root(v);
		}
		public void print() {
			for (int i=0; i<uf.length; i++) {
				p(uf[i]+" ");
			}
			pln("");
		}
	}
	class Point {
		int x;
		int y;
		public Point(int x, int y) {
			this.x = x;
			this.y = y;
		}
		public Point(Point pt) {
			this.x = pt.x;
			this.y = pt.y;
		}
		public boolean equals(Object o) {
			if (o instanceof Point) {
				Point that = (Point)o;
				return (x == that.x) && (y == that.y);
			}
			return false;
		}
		public int hashCode() {
			return x + (y << 16);
		}
		public String toString() {
			return "(" + x + ", " + y + ")";
		}
	}
	class Info implements Comparable<Info> {
		int idx;
		int val;
		public Info(int idx, int val) {
			this.idx = idx;
			this.val = val;
		}
		public int compareTo(Info o) {
			return idx - o.idx;
		}
		public boolean equals(Object o) {
			if (o instanceof Info) {
				Info that = (Info)o;
				return 0 == compareTo(that);
			}
			return false;
		}
		public int hashCode() {
			return idx + (val << 16);
		}
		public String toString() {
			return "(" + idx + ", " + val + ")";
		}
	}
	class InfoComp implements Comparator<Info> {
		public int compare(Info o1, Info o2) {
			return o1.val - o2.val;
		}
	}
	int pint(String s) {
		return Integer.parseInt(s);
	}
	String readLine() {
		try {
			_line = _in.readLine();
			return _line;
		} catch (IOException e) {
			throw new RuntimeException(e);
		}
	}
	int readNum() {
		readLine();
		return pint(_line);
	}
	String[] readFlds() {
		readLine();
		_flds = _line.split(" ");
		return _flds;
	}
	int[] readNums() {
		readFlds();
		_nums = new int[_flds.length];
		for (int i=0; i<_flds.length; i++) {
			_nums[i] = pint(_flds[i]);
		}
		return _nums;
	}
	void p(char c) {
		_out.print(c);
	}
	void pln(char c) {
		_out.println(c);
	}
	void p(double d) {
		_out.print(d);
	}
	void pln(double d) {
		_out.println(d);
	}
	void p(long l) {
		_out.print(l);
	}
	void pln(long l) {
		_out.println(l);
	}
	void p(String s) {
		_out.print(s);
	}
	void pln(String s) {
		_out.println(s);
	}
	String _line;
	String[] _flds;
	int[] _nums;
	static BufferedReader _in;
	static PrintWriter _out;
	public static void main(String[] args) {
		long start = System.currentTimeMillis();
		_in = new BufferedReader(new InputStreamReader(System.in));
		_out = new PrintWriter(System.out);
		new Main().solve();
		_out.flush();
		long end = System.currentTimeMillis();
		if (bElapsed) {
			System.err.println((end-start) + "ms");
		}
	}
}