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)

def nxt(arr)
	arr.each do |val|
		unless $grp[val]
			return val
		end
	end
	return nil
end

def dfs_src(s,id)
	stk = [s]
	$grp[s] = id
	while stk != []
		u = nxt($l[stk.last])
		if u
			stk.push(u)
			$grp[u] = id
		else
			stk.pop
		end
	end
end
$grp = []

result = []
$l=[]
n, m = gets.chomp.split(" ").map(&:to_i)
m.times do
	s,t = gets.chomp.split(" ").map(&:to_i)
	if $l[s]
		$l[s].push(t)
	else
		$l[s] = [t]
	end
	if $l[t]
		$l[t].push(s)
	else
		$l[t] = [s]
	end
end
q = gets.chomp.to_i

list = []
i = 0
while i <= n
	unless $grp[i]
		if $l[i]
			dfs_src(i, i)
		end
	end
	i += 1
end

q.times do
	res = "no"
	s, t = gets.chomp.split.map(&:to_i)
	if $grp[s] == $grp[t] && $grp[s] != nil
		result.push("yes")
	else
		result.push("no")
	end
end

result.each do |r|
	puts r
end