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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <stdlib.h>

typedef struct ll{
  int *data;
  int num;
  struct ll *next;
} DL;

DL *createList(int *data, int n){
  DL *new;
  new = (DL *)malloc(sizeof(DL));
  int i;
  new->data = (int *)malloc(sizeof(int) * n);
  for(i=0; i<n; i++){
    new->data[i] = data[i];
  }
  new->num = n;

  return new;
}

void addList(DL **head, DL *add){
  add->next = *head;
  *head = add;
  return;
}

void deleteList(DL **pt){
  DL *del = *pt;
  *pt = del->next;

  free(del->data);
  free(del);
  return;
}

void printList(DL *head){
  int i, n, *data;
  puts("LIST---------------");
  while(head != NULL){
    n = head->num;
    data = head->data;
    for(i=0; i<n; i++) printf("%d ", data[i]);
    putchar('\n');
    head = head->next;
  }
  puts("---------------LIST");
  return;
}

int main()
{
  int M, N;
  int i, j, n, index, flg, find;
  int *ss;
  int data[10000]={0};
  int node[10000];

  DL *head=NULL;
  DL **search = NULL;
  scanf("%d%d", &N, &M);

  scanf("%d", &n);
  for(i=0; i<n; i++){
    scanf("%d", &index);
    data[index]++;
  }

  for(i=1; i<N; i++){
    scanf("%d", &n);
    find=0;
    for(j=0; j<n; j++){
      scanf("%d", node+j);
      if(data[node[j]]) find++;
    }
    if(find){
      for(j=0; j<n; j++){
        data[node[j]]=1;
      }
    }else{
      DL *add = createList(node, n);
      addList(&head, add);
    }
  }

  flg = 1;
  while(flg && head != NULL){
    search = &head;
    flg = 0;
    while(*search != NULL){
      n = (*search)->num;
      ss = (*search)->data;
      find=0;
      for(i=0; i<n; i++){
        if(data[ss[i]]) find++;
      }
      if(find){
        for(i=0; i<n; i++){
          data[ss[i]]=1;
        }
        deleteList(search);
        flg++;
      }else search = &(*search)->next;
    }
  }
  printf("%s\n", head==NULL?"YES":"NO");
  return(0);
}