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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#include <sys/time.h>

#define mp       make_pair
#define mt  make_tuple
#define rep(i,n) for(int i=0;i<(n);i++)

using namespace std;

using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;

const int INF=1<<29;
const double EPS=1e-9;
const ll MOD = 1000000007;

const int dx[]={1,0,-1,0},dy[]={0,-1,0,1};

const int MAX_NM = 100100;
int N,M;

vector<int> learn_person[MAX_NM];
vector<int> edges[MAX_NM];

bool visited[MAX_NM];
class Timer {
public:
  Timer() {}
  void start() { start_time = get_mill_sec(); }
  double get_mill_duration() { return get_mill_sec() - start_time; }

private:
  double start_time;
  double get_mill_sec() {
    struct timeval res;
    gettimeofday(&res, NULL);
    return res.tv_sec * 1000 + res.tv_usec / 1000;
  }
};
int cnt_N;
Timer timer;
bool timeout;
void dfs(int pos){
  visited[pos] = true;
  if (timeout)return ;
  if (timer.get_mill_duration() >= 150){
    timeout = true;
    return ;
  }
  for (const auto &lang : edges[pos]){
    if (timeout)return ;
    for (const auto &next : learn_person[lang]){

      if (visited[next])continue;
      dfs(next);
    }
  }
}


int main(){
  timer.start();
  timeout = false;
  cin.tie(0);
  ios::sync_with_stdio(false);
  cin >> N >> M;
  cnt_N = N;
  set<int> learn_lang;
  for (int i = 0; i < N; i++){
    int K;
    cin >> K;
    for (int j = 0; j < K; j++){
      int l;
      cin >> l;
      l--;
      learn_person[l].emplace_back(i);
      edges[i].emplace_back(l);
    }
  }
  dfs(0);
  bool ok = true;
  for (int i = 0; i < N; i++){
    if (not visited[i]){
      ok = false;
    }
  }
  if (ok){
    cout << "YES" << endl;
  }else{
    cout << "NO" << endl;
  }

  return 0;
  
}