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)

require('set')

def freind_search(matrix)
	visited = Set[]
	search = lambda do |base, target|
		return true if base == target

		queue = [].push(base)
		until queue.empty?
			v = queue.shift
			visited.add(v)

			found = matrix[v].each_index.
				select { |i| matrix[v][i] && !visited.include?(i) }.
				each { |i| queue.push(i) }.
				find { |i| i == target }

			if found
				matrix[v][found] = true
				return true
			end
		end

	end
end

n, m = STDIN.gets.split.map(&:to_i)
matrix = Array.new(n) { Array.new(n, false) }

m.times do
	vertex, freind = STDIN.gets.split.map(&:to_i)
	matrix[vertex][freind] = matrix[freind][vertex] = true
end

questions = STDIN.gets.to_i
questions.times do
	a, b = STDIN.gets.split.map(&:to_i)
	puts freind_search(matrix).call(a, b) ? "yes" : "no"
end