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# (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Text;

namespace Graph_I
{
    class Connected_Components
    {
        static int[] Cycle;

        static void Main(string[] args)
        {

            var nm = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            var n = nm[0];
            var m = nm[1];
            Cycle = Enumerable.Range(0, n).ToArray();

            for (int i = 0; i < m; i++)
            {
                var st = Console.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();
                var s = st[0];
                var t = st[1];
                if (s < t) Connect(s, t);
                else Connect(t, s);
            }


            var q = int.Parse(Console.ReadLine());

            var str = new StringBuilder();
            for (int i = 0; i < q; i++)
            {
                var st = Console.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();
                str.AppendLine((IsConnect(st[0], st[1]) ? "yes" : "no"));
            }

            Console.Write(str.ToString());
        }

        static void Connect(int s, int t)
        {
            if (IsConnect(s, t)) return;

            var sp = Cycle[s];
            while (true)
            {
                if (Cycle[sp] == s) break;
                sp = Cycle[sp];
            }
            Cycle[sp] = t;
            Cycle[t] = s;
        }

        static bool IsConnect(int s, int t)
        {
            int sp = s;
            while ((sp = Cycle[sp]) != s)
                if (sp == t) return true;

            return false;
        }
    }
}