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 <iostream>
#include <cstdio>
#include <string>
#include <algorithm>
#include <utility>
#include <cmath>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <numeric>
#include <functional>
using namespace std;
typedef long long ll;
typedef vector<ll> vl;
typedef vector<vector<ll>> vvl;
typedef pair<ll, ll> P;
#define rep(i, n) for(ll i = 0; i < n; i++)
#define exrep(i, a, b) for(ll i = a; i <= b; i++)
#define out(x) cout << x << endl
#define exout(x) printf("%.10f\n", x)
#define chmax(x, y) x = max(x, y)
#define chmin(x, y) x = min(x, y)
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define pb push_back
#define re0 return 0
const ll mod = 1000000007;
const ll INF = 1e16;
const ll MAX_N = 100010;

class UnionFind {
public:
    vl parent;  // 親ノード
    vl Siz;  // 集合の大きさ
    
    // コンストラクタ
    UnionFind(ll n): parent(n), Siz(n, 1) {
        rep(i, n) {
            parent[i] = i;
        }
    }

    // n要素で初期化
    void init(ll n) {
        parent.resize(n);
        Siz.assign(n, 1);
        rep(i, n) {
            parent[i] = i;
        }
    }

    // xの属する集合の根を求める
    ll root(ll x) {
        if(parent[x] == x) {
            return x;
        }
        else {
            return parent[x] = root(parent[x]);
        }
    }

    // xとyの属する集合を併合
    void unite(ll x, ll y) {
        x = root(x);
        y = root(y);
        if(x == y) {
            return;
        }
        if(Siz[x] < Siz[y]) {
            swap(x, y);
        }
        Siz[x] += Siz[y];
        parent[y] = x;
    }
    
    // xとyが同じ集合に属するかどうか
    bool same(ll x, ll y) {
        return root(x) == root(y);
    }

    // xの属する集合の要素数を求める
    ll size(ll x) {
        return Siz[root(x)];
    }
};
 
int main() {
    ll n, m;
    cin >> n >> m;

    UnionFind Uni(n+m);
    Uni.init(n+m);
    rep(v, n) {
        ll k;
        cin >> k;
        rep(i, k) {
            ll L;
            cin >> L;
            L--;
            Uni.unite(v, n+L);
        }
    }

    set<ll> st;
    rep(v, n) {
        st.insert(Uni.root(v));
    }
    
    if(st.size() == 1) {
        out("YES");
    }
    else {
        out("NO");
    }
    
    re0;
}