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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)


import scala.collection.mutable
import scala.collection.mutable.ArrayBuffer

/**
 * Created by sonetsuyoshi on 2015/12/16.
 */
case class Person(id: Int, langs: Seq[Int])

object Main extends App {
  val params = readLine.split(" ").map(_.toInt)
  val N = params(0)
  val M = params(1)

  val langs: Array[mutable.MutableList[Person]] = Array.fill(M)(mutable.MutableList[Person]())
  val ps = 0.until(N).map(x => {
    val p = Person(x, readLine.split(" ").drop(1).map(_.toInt - 1))
    p.langs.foreach(l => langs(l).+=(p))
    p
  })
  val p0 = ps(0)

  val unvisitedPersons = Array.fill(N)(true)
  val unvisitedLangs = Array.fill(M)(true)

  val visitingPersons = mutable.Stack[Person]()
  val visitingLangs = mutable.Stack[Int]()

  visitingPersons.push(p0)

  while(visitingPersons.size > 0) {
    val p = visitingPersons.pop()
    p.langs.filter(l => unvisitedLangs(l)).foreach(l => {
      unvisitedLangs(l) = false
      val pps = langs(l)
      pps.filter(pp => unvisitedPersons(pp.id)).foreach(pp => {
        unvisitedPersons(pp.id) = false
        visitingPersons.push(pp)
      })
    })
  }
  if(unvisitedPersons.forall(_ == false)) {
    println("YES")
  } else {
    println("NO")
  }
}