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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.CodeDom;
using System.Collections.Generic;
using System.Configuration;
using System.Diagnostics.CodeAnalysis;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Xml.Schema;

namespace AtCoder
{
    public static class Ex
    {
        public static List<string> FastSort(this List<string> s) { s.Sort(StringComparer.OrdinalIgnoreCase); return s.ToList(); }
        public static void yesno(this bool b) { Console.WriteLine(b ? "yes" : "no"); }
        public static void YesNo(this bool b) { Console.WriteLine(b ? "Yes" : "No"); }
        public static void YESNO(this bool b) { Console.WriteLine(b ? "YES" : "NO"); }

        public static int PopCount(this int bits)
        {
            bits = (bits & 0x55555555) + (bits >> 1 & 0x55555555);
            bits = (bits & 0x33333333) + (bits >> 2 & 0x33333333);
            bits = (bits & 0x0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f);
            bits = (bits & 0x00ff00ff) + (bits >> 8 & 0x00ff00ff);
            return (bits & 0x0000ffff) + (bits >> 16 & 0x0000ffff);
        }
    }

    partial class AtCoder
    {
        public string GetStr() { return Console.ReadLine().Trim(); }
        public char GetChar() { return Console.ReadLine().Trim()[0]; }
        public int GetInt() { return int.Parse(Console.ReadLine().Trim()); }
        public long GetLong() { return long.Parse(Console.ReadLine().Trim()); }
        public double GetDouble() { return double.Parse(Console.ReadLine().Trim()); }
        public string[] GetStrArray() { return Console.ReadLine().Trim().Split(' '); }
        public int[] GetIntArray() { return Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray(); }
        public long[] GetLongArray() { return Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray(); }
        public char[] GetCharArray() { return Console.ReadLine().Trim().Split(' ').Select(char.Parse).ToArray(); }
        public double[] GetDoubleArray() { return Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray(); }
        public T[][] CreateJaggedArray<T>(int H, int W, T value) { return Enumerable.Repeat(0, H).Select(s => Enumerable.Repeat(value, W).ToArray()).ToArray(); }
        public int[][] GetIntJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetIntArray().ToArray()).ToArray(); }
        public long[][] GetLongJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetLongArray().ToArray()).ToArray(); }
        public char[][] GetCharJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetStr().ToCharArray()).ToArray(); }
        public double[][] GetDoubleJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetDoubleArray()).ToArray(); }

        Dictionary<int, List<int>> GetUnweightedAdjacencyList(int N, int M, bool isDirected, bool isNode_0indexed)
        {
            var dic = new Dictionary<int, List<int>>();
            foreach (var e in Enumerable.Range(0, N)) { dic.Add(e, new List<int>()); }
            for (int i = 0; i < M; i++)
            {
                var input = GetIntArray();
                var a = isNode_0indexed ? input[0] : input[0] - 1;
                var b = isNode_0indexed ? input[1] : input[1] - 1;
                dic[a].Add(b);
                if (isDirected == false) dic[b].Add(a);
            }
            return dic;
        }
        Dictionary<int, List<Edge>> GetWeightedAdjacencyList(int N, int M, bool isDirected, bool isNode_0indexed)
        {
            var dic = new Dictionary<int, List<Edge>>();
            foreach (var e in Enumerable.Range(0, N)) { dic.Add(e, new List<Edge>()); }
            for (int i = 0; i < M; i++)
            {
                var input = GetIntArray();
                var a = isNode_0indexed ? input[0] : input[0] - 1;
                var b = isNode_0indexed ? input[1] : input[1] - 1;
                var c = input[2];
                dic[a].Add(new Edge(b, c));
                if (isDirected == false) dic[b].Add(new Edge(a, c));
            }
            return dic;
        }

        bool eq<T, U>() => typeof(T).Equals(typeof(U));
        T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
        T cv<T>(string s) => eq<T, int>() ? ct<T, int>(int.Parse(s))
                           : eq<T, long>() ? ct<T, long>(long.Parse(s))
                           : eq<T, double>() ? ct<T, double>(double.Parse(s))
                           : eq<T, char>() ? ct<T, char>(s[0])
                                             : ct<T, string>(s);
        void Multi<T>(out T a) => a = cv<T>(GetStr());
        void Multi<T, U>(out T a, out U b)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]);
        }
        void Multi<T, U, V>(out T a, out U b, out V c)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
        }
        void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
        }
        void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);
        }
        void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]);
        }
    }

    class Pair : IComparable<Pair>
    {
        public Pair(int node, long cost)
        {
            Node = node; Cost = cost;
        }
        public int Node { get; set; }
        public long Cost { get; set; }
        public int CompareTo(Pair p)
        {
            return p.Cost > Cost ? 1 : -1;
        }
    }

    class Edge
    {
        public Edge(int to, long length)
        {
            To = to;
            Length = length;
        }
        public int To { get; set; }
        public long Length { get; set; }
    }

    class Comparable : IComparable<Comparable>
    {
        public Comparable(int value)
        {
            Value = value;
        }

        public int Value { get; set; }
        public int CompareTo(Comparable c)
        {
            var a = Math.Abs(Value);
            var b = Math.Abs(c.Value);
            return a > b ? 1 : a == b ? 0 : -1;
        }
    }

    class Comparer<T> : IComparer<T>
    {
        public int Compare(T t1, T t2)
        {
            return 1;
        }
    }



    partial class Program
    {
        static void Main()
        {
            Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
            new AtCoder().Solve();
            Console.Out.Flush();
            Console.Read();
        }
    }

    public partial class AtCoder
    {
        public void Solve()
        {
            int N;int M;
            Multi(out N, out M);
            var G = new Dictionary<int, List<int>>();
            for (int i = 0; i < N + M; i++) G.Add(i, new List<int>());
            for(int i = 0; i < N; i++)
            {
                foreach(var l in GetIntArray().Skip(1))
                {
                    G[i].Add(N+l-1);
                    G[N + l-1].Add(i);
                }   
            }

            var dist = new int[N+M].Select(s => -1L).ToArray();
            var queue = new Queue<int>();
            dist[0] = 0;
            queue.Enqueue(0);
            while (queue.Count() > 0)
            {
                var now = queue.Dequeue();
                foreach (var next in G[now])
                {
                    if (dist[next] != -1) continue;
                    dist[next] = dist[now] + 1;
                    queue.Enqueue(next);
                }
            }
            dist.Take(N).All(a => a!=-1).YESNO();
        }
    }
}