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)

n, m = gets.split.map(&:to_i)
v = Array.new n
g = Array.new(n) { [] }
m.times do
  s, t = gets.split.map(&:to_i)
  g[s] << t
  g[t] << s
end
n.times do |u|
  next if v[u]
  v[u] = u
  stack = [u]
  until stack.empty?
    s = stack.pop
    v[s] = u
    g[s].each do |t|
      stack.push t unless v[t]
    end
  end
end
gets.to_i.times do
  s, t = gets.split.map(&:to_i)
  puts v[s] == v[t] ? 'yes' : 'no'
end