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)

def depth_first_search a_list, st, v_group, cnt
  while st.length > 0
    i = st.last
    v_group[i] = cnt
    found = false
    a_list[i].each do |a|
      unless v_group[a]
        st.push(a)
        found = true
        break
      end
    end
    st.pop unless found
  end
end

users_count, n = gets.chomp.split(' ').map(&:to_i)

a_list = Array.new(users_count).map{|m| []} # 隣接リスト
n.times do
  i, j = gets.chomp.split(' ').map(&:to_i)
  a_list[i].push(j)
  a_list[j].push(i)
end

v_group = Array.new(users_count, false) # 頂点のグループ分け
cnt = 1
0.upto(users_count - 1) do |i|
  next if v_group[i]
  depth_first_search(a_list, [i], v_group, cnt)
  cnt += 1
end
q_cnt = gets.chomp.to_i
ans = []
q_cnt.times do
  f1, f2 = gets.chomp.split(' ').map(&:to_i)
  ans.push((v_group[f1] && v_group[f1] == v_group[f2]) ? 'yes' : 'no')
end
puts ans.join("\n")