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: Runtime Error)

# definition
n, m = gets.split.map { |i| i.to_i }
@list = Array.new(n).map { [] }
m.times do
  s, t = gets.split.map { |i| i.to_i }
  @list[s] << t
  @list[t] << s
end

def init
  @result = false
  @d = []
end

def d_search(i, j)
  @d[i] = true
  @result = true if i == j
  return if @result
  @list[i].each do |k|
    d_search(k, j) unless @d[k]
  end
end

# main
q = gets.to_i
q.times do
  s, t = gets.split.map { |i| i.to_i }
  init
  d_search(s, t)
  puts @result ? "yes" : "no"
end