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)

# -*- coding: utf-8 -*-

def assignColor(G):
    n = len(G)
    C = [-1 for i in range(n)]
    for i in range(n):
        if C[i] == -1:
            C = BFS(G, i, C)
    return C
        
def BFS(G, start, C):
    n = len(G)
    flag = [0] * n
    Q = []

    Q.append(start)
    C[start] = start
    flag[start] = 1

    while len(Q) != 0:
        u = Q.pop(0)
        v = [i for i in G[u] if flag[i] == 0] # v := ??£??\???????????????????????¢?´¢??????????????????
        
        for i in v:
            Q.append(i)
            C[i] = C[start]
            flag[i] = 1
    
    return C

def main():
    
    n, m = list(map(int, input().split()))
    G = [[] for i in range(n)]

    for i in range(m):
        s, t = list(map(int, input().split()))
        G[s].append(t)
        G[t].append(s)

    C = assignColor(G)
        
    q = int(input())
    
    for i in range(q):
        s, t = list(map(int, input().split()))
        if C[s] == C[t]:
            print("yes")
        else:
            print("no")
            
if __name__ == "__main__":
    main()