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 Ruby (judge verdict: Runtime Error)

class MyGraph
  attr_accessor :vec,:colors

  def initialize(n)
    @vec = Array.new(n).map{Array.new()}
    @colors = Array.new(n,-1)
  end

  def create_link(i,j)
    @vec[i].push(j)
    @vec[j].push(i)
  end

  def find_friend(i,j)
    if i>@colors.length or j>colors.length
      return "no"
    end

    if @colors[i]==@colors[j]
      return "yes"
    else
      return "no"
    end
  end

  def paint(i,color)
    if @colors[i]==-1
      @colors[i]=color
    else
      return
    end

    @vec[i].each do |v|
      self.paint(v,color)
    end
  end
end

n,m = STDIN.gets().split(' ').map{ |i| i.to_i}

graph = MyGraph.new(n)

m.times do 
  x, y = STDIN.gets().split(' ').map{ |i| i.to_i }
  graph.create_link(x,y)
end

n.times do |i|
  graph.paint(i,i)
end

q = STDIN.gets().to_i
q.times do
  i,j = STDIN.gets().split(' ').map{ |k| k.to_i }
  print "#{graph.find_friend(i,j)}\n"
end