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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdio.h>

int find(int x);
void f_union(int x, int y);

int G[1001];

typedef struct {
    int K;
    unsigned char lang[1001];
}CODER;

CODER player[1001] = {0};

int main(void)
{
    int N, M, K;
    int i, j, k, l;

    scanf("%d %d", &N, &M);

    for (i = 0; i < N; i++) {
        scanf("%d", &K);
        player[i].K = K;
        G[i] = i;
        for (k = 0; k < player[i].K; k++)
            scanf("%d", &player[i].lang[k]);
    }

    for (i = 0; i < N; i++)
        for (j = 0; j < player[i].K; j++)
            for (k = i+1; k < N; k++)
                for (l = 0; l < player[k].K; l++)
                    if (player[i].lang[j] == player[k].lang[l])
                        f_union(G[i], G[k]);

    for (i = 1; i < N; i++) {
        if (find(G[0]) != find(G[i])) {
            printf("NO");
            return 0;
        }
    }
    printf("YES");
    return 0;
}

int find(int x)
{
    return (G[x]==x)?(x):(G[x] = find(G[x]));
}

void f_union(int x, int y)
{
    x = find(x);
    y = find(y);
    if (x == y) return;
    G[x] = y;
}