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: Accepted)

#-- グループ分けされてない隣接ノード番号を返す
def next_neighbor nodes, x
  nodes[x][:neighbors].each do |neighbor|
    return neighbor if nodes[neighbor][:group_id] == nil
  end
  nil
end

#-- メイン処理開始
n, m = gets.split.map(&:to_i)
nodes = Array.new(n) do {neighbors: []} end

#-- 隣接リストを格納
m.times do
  f_node, t_node = gets.split.map(&:to_i)
  nodes[f_node][:neighbors] << t_node
  nodes[t_node][:neighbors] << f_node
end

#-- グループ分けされていないノードに関してDFSする
group_id = 0; stack = []
nodes.each_with_index do |node, i|
  if node[:group_id] == nil
    stack.push i; group_id += 1
    while stack != []
      x = stack.last
      neighbor = next_neighbor nodes, x
      if neighbor
        stack.push neighbor
        nodes[neighbor][:group_id] = group_id
      else
        stack.pop
      end
    end
  end
end

#-- 判定して出力
c = gets.to_i
c.times do
  f_node, t_node = gets.split.map(&:to_i)
  f = nodes[f_node][:group_id]
  t = nodes[t_node][:group_id]

  if f == nil || t == nil || f != t then puts "no" else puts "yes" end
end