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 Python3 (judge verdict: Time Limit Exceeded)

import sys

sys.setrecursionlimit(1000000)

n, m = map(int, input().split())
g = [set() for _ in range(n)]

while m:
    s, t = map(int, input().split())
    g[s].add(t)
    g[t].add(s)
    m -= 1


def find(s, t):
    global g
    visited = [0] * n

    def dfs(i):
        visited[i] = 1
        if i == t:
            return True
        for f in g[i]:
            if not visited[f]:
                if dfs(f):
                    return True
        return False

    return dfs(s)


q = int(input())
while q:
    s, t = map(int, input().split())
    print('yes' if find(s, t) else 'no')
    q -= 1