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: Time Limit Exceeded)

def breadth_first_search(s, rel_tbl, checked)
  ans = [s]
  checked[s] = 1
  q = [s]
  loop do
    break if q.size == 0
    next_q = []
    q.each{|i|
      rel_tbl[i].each{|j|
        if checked[j] < 0 then
          rel_tbl[s] << j
          checked[j] = 1
          next_q << j
          ans << j
        end
      }
    }
    q = next_q
  end
  return ans
end

n, m = gets.split.map(&:to_i)

rel_tbl = Array.new(n){[]}
checked = Array.new(n){-1}

m.times{
  i, j = gets.split.map(&:to_i)
  rel_tbl[i] << j
  rel_tbl[j] << i
}


q = gets.to_i
q.times{
  s, t = gets.split.map(&:to_i)
  checked = Array.new(n){-1}
  if breadth_first_search(s, rel_tbl, checked).index(t)
    puts "yes"
  else
    puts "no"
  end
}