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 User
  attr_reader :id
  def initialize(id)
    @id = id
    @root = true
    @parent = self
  end

  def connect(other)
    if @parent == self
      @parent = other.union
    else
      @parent.union.connect(other.union)
    end
  end

  def union
    @parent = @parent.union if @parent != self
    return @parent
  end

  def ==(other)
    @id == other.id
  end

  def inspect
    @id
  end
  
end
def main
  n, m = gets.split(" ").map(&:to_i)
  user = Array.new(n){|i|User.new(i)}
  m.times do
    arg = gets.split(" ").map(&:to_i)
    user[arg[0]].connect(user[arg[1]])
  end
  gets.to_i.times do
    arg = gets.split(" ").map(&:to_i)
    if user[arg[0]].union == user[arg[1]].union
      puts "yes"
    else
      puts "no"
    end
  end
end
main