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: Time Limit Exceeded)

# Node
class Node
  attr_accessor :id, :edges, :visited

  def initialize(id, edges = [], visited = false)
    @id, @edges, @visited = id, edges, visited
  end
end

# Edge
class Edge
  attr_accessor :to

  def initialize(to)
    @to = to
  end
end

# Graph
class Graph
  attr_accessor :nodes

  def initialize(data)
    @nodes = data.each_with_object({}) do |(id, edges), hash|
      edges.map! { |edge| Edge.new(*edge) }
      hash[id] = Node.new(id, edges)
    end
  end

  def connected?(s, t)
    @nodes.each do |id, node|
      node.visited = false
    end

    queue = [s]

    while queue.any?
      id = queue.shift
      node = @nodes[id]
      node.visited = true
      node.edges.each do |edge|
        id = edge.to
        visited_node = @nodes[id]
        return true if visited_node.id == t
        queue << visited_node.id unless visited_node.visited
      end
    end

    false
  end
end

n, m = gets.chop.split.map(&:to_i)

data = {}

n.times do |i|
  data[i] = []
end

m.times do
  s, t = gets.chop.split.map(&:to_i)
  data[s] << t
  data[t] << s
end

g = Graph.new data

q = gets.chop.to_i

q.times do
  puts (g.connected?(*gets.chop.split.map(&:to_i))) ? 'yes' : 'no'
end