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)

Vertex = Struct.new(:id, :adjacencies, :group)

def grouping!(vertex, group)
	return unless vertex.group.nil?
	vertex.group = group
	vertex.adjacencies.each { |v| grouping!(v, group) }
end

n, m = STDIN.gets.split.map(&:to_i)
vertex_list = Array.new(n) { |i| Vertex.new(i, []) }
m.times do
	vertex_id, friend_id = STDIN.gets.split.map(&:to_i)
	vertex_list[vertex_id].adjacencies << vertex_list[friend_id]
	vertex_list[friend_id].adjacencies << vertex_list[vertex_id]
end

vertex_list.each_with_index { |v, i| grouping!(v, i) }

q = STDIN.gets.to_i
q.times do
	a, b = STDIN.gets.split.map(&:to_i)
	puts vertex_list[a].group == vertex_list[b].group ? "yes" : "no"
end