Problem:
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Connected Components

Write a program which reads relations in a SNS (Social Network Service), and judges that given pairs of users are reachable each other through the network.

Input

In the first line, two integer $n$ and $m$ are given. $n$ is the number of users in the SNS and $m$ is the number of relations in the SNS. The users in the SNS are identified by IDs $0, 1, ..., n-1$.

In the following $m$ lines, the relations are given. Each relation is given by two integers $s$ and $t$ that represents $s$ and $t$ are friends (and reachable each other).

In the next line, the number of queries $q$ is given. In the following $q$ lines, $q$ queries are given respectively. Each query consists of two integers $s$ and $t$ separated by a space character.

Output

For each query, print "yes" if $t$ is reachable from $s$ through the social network, "no" otherwise.

Constraints

$2 \leq n \leq 100,000$

$0 \leq m \leq 100,000$

$1 \leq q \leq 10,000$

Sample Input

10 9
0 1
0 2
3 4
5 7
5 6
6 7
6 8
7 8
8 9
3
0 1
5 9
1 3

Sample Output

yes
yes
no

Solution in Scala (judge verdict: Wrong Answer)

import scala.collection.mutable
import scala.io.StdIn._

case class Edge(from: Int, to: Int)

object Main extends App {
  val Array(n, m) = readLine().split(" ").map(_.toInt)
  val reached: mutable.Seq[Set[Int]] = mutable.Seq.fill(n)(Set())
  var edges: Set[Edge] = Set()

  for (i <- 1 to m) {
    val Array(from, to) = readLine().split(" ").map(_.toInt)
    reached(from) += to
    reached(to) += from
    edges += Edge(from, to)
    edges += Edge(to, from)
  }

  for (i <- 1 to readInt()) {
    val Array(f, t) = readLine().split(" ").map(_.toInt)
    if (canReach(f, t)) println("yes") else println("no")
  }

  def canReach(from: Int, to: Int): Boolean = {
    if (reached(from) contains to) return true

    val queue: mutable.Queue[Edge] = mutable.Queue()
    edges.collectFirst {
      case e@Edge(f, _) if f == from => queue.enqueue(e)
    }

    while (queue.nonEmpty) {
      val edge = queue.dequeue()
      edges -= edge

      if (reached(edge.from) contains to) {
        reached(from) += to
        return true
      }

      edges.foreach(e => {
        if (e.from == edge.from || e.from == edge.to) {
          reached(from) += e.to
          reached(e.to) += from
          reached(edge.from) += e.to
          reached(e.to) += edge.from
          if (e.to == to) return true
          queue.enqueue(e)
        }
      })
    }

    false
  }
}