Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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: Wrong Answer)

class Node
  def initialize(id)
    @id = id
    @friends = []
    @visited = false
  end

  attr_accessor :id, :friends, :visited
end

def input_pair(id1, id2, pool)
  me = pool[id1]
  other = pool[id2]
  me = pool[id1] = Node.new(id1) if me == nil
  other = pool[id2] = Node.new(id2) if other == nil

  me.friends << id2
  other.friends << id1
end

def visit(current, target, pool)
  pool[current].visited = true
  if (current == target) then
    return true
  end

  unvisit_friends = 
    pool[current].friends.select {|item| pool[item].visited == false}

  if (unvisit_friends.size == 0) then
    return false
  end

  return unvisit_friends.any? do |item|
    visit(item, target, pool)
  end
end


# main
n, m = gets.chomp.split.map(&:to_i)
pool = {}
(n).times do |i|
  pool[i] = Node.new(i)
end
(m).times do
  inputs = gets.chomp.split.map(&:to_i)
  input_pair(inputs[0], inputs[1], pool)
end

(gets.chomp.to_i).times do 
  inputs = gets.chomp.split.map(&:to_i)
  puts "#{visit(inputs[0], inputs[1], pool) ? "yes" : "no"}"
end