Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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)

UNDEF = -1



def dfs(r, c)
	s = [r]
	$color[r] = c
	
	while not s.empty?
		u = s.pop
		$g[u].size.times do |i|
			v = $g[u][i]
			if $color[v] == UNDEF
				$color[v] = c
				s.push(v)
			end
		end
	end
end



def assignColor()
	id = 1
	$color = Array.new($n, UNDEF)
	$n.times do |u|
		if $color[u] == UNDEF
			dfs(u, id)
			id += 1
		end
	end
end



$n, m = gets.split.map &:to_i
$g = Array.new($n){ Array.new(0) }

m.times do
	s, t = gets.split.map &:to_i
	$g[s].push(t)
	$g[t].push(s)
end

assignColor()

q = gets.to_i

q.times do
	s, t = gets.split.map &:to_i
	if $color[s] == $color[t]
		puts "yes"
	else
		puts "no"
	end
end