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 C++11 (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <vector>
#define eol '\n'
using namespace std;

vector<int> group;

void bfs(int v, int g, vector< vector<int> > list) {
  if (group[v] != 0) {
    return;
  }
  group[v] = g;
  for (int i = 0; i < list[v].size(); i++) {
    bfs(list[v][i], g, list);
  }
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);

  int n,m,s,t,q;
  cin >> n >> m;

  vector< vector<int> > list(n, vector<int>());
  group = vector<int>(n,0);
  
  for (int i = 0; i < m; i++) {
    cin >> s >> t;
    list[s].push_back(t);
    list[t].push_back(s);
  }

  int g = 1;
  for (int i = 0; i < n; i++) {
    if (group[i] == 0) {
      bfs(i, g, list);
      g++;
    }
  }

  cin >> q;
  for (int i = 0; i < q; i++) {
    cin >> s >> t;
    if (group[s] == group[t]) {
      cout << "yes" << eol;
    } else {
      cout << "no" << eol;
    }
  }
  return 0;
}