Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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)

def bfs(adj, s):
    n = len(adj)
    d = [-1 for _ in range(n)]
    c = [0 for _ in range(n)]

    d[s] = 0
    c[s] = 1

    queue = [s]

    while len(queue) > 0:
        u = queue.pop(0)
        for v in adj[u]:
            if c[v] == 0:
                c[v] = 1
                d[v] = d[u] + 1
                queue.append(v)

    return d


s = [int(x) for x in input().split()]
n = s[0]
m = s[1]
adj = [[] for _ in range(n)]
for _ in range(m):
    s = [int(x) for x in input().split()]
    adj[s[0]].append(s[1])
    adj[s[1]].append(s[0])

q = int(input())
for _ in range(q):
    s = [int(x) for x in input().split()]
    u = s[0]
    v = s[1]
    d = bfs(adj, u)
    if d[v] > 0:
        print("yes")
    else:
        print("no")