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: Wrong Answer)

N, M = gets.split.map &:to_i
$parent = []

def trace_parent i
  stack = []
  t = i
  loop{
    if $parent[t]
      stack << t
      t = $parent[t]
    else
      break
    end
  }
  stack.each{|e|
    $parent[e] = t
  }
  t
end

M.times{
  s, t = gets.split.map &:to_i
  if $parent[s] == nil
    if $parent[t] == nil
      $parent[t] = s
    else
      root = trace_parent(t)
      $parent[s] = root
      $parent[t] = root
    end
  elsif $parent[t] == nil
    root = trace_parent(s)
    $parent[s] = root
    $parent[t] = root
  else
    s_root = trace_parent(s)
    $parent[t] = s_root
  end
}
gets.to_i.times{
  s, t = gets.split.map &:to_i
  puts trace_parent(s) == trace_parent(t) ? :yes : :no
}