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: Wrong Answer)

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

def are_connected(s, t):
    q = [s]
    checked = [False] * n
    checked[s] = True

    while q:
        user = q.pop(0)
        for f in friend[user]:
            if f == t:
                print(f, user)
                return True
            elif not checked[f]:
                q.append(f)
                checked[f] = True
    return False

q = int(input())
for i in range(q):
    s, t = map(int, input().split())
    if are_connected(s, t):
        print('yes')
    else:
        print('no')