Communicating Servers

You are given n servers and a list of m direct links connecting pairs of them. Two servers can communicate if there exists a series of direct links connecting them. For each of the q queries, determine whether a given pair of servers can communicate.

The connectivity can be expressed mathematically using the Union-Find data structure, where the condition for two servers a and b to communicate is given by:

\(find(a) = find(b)\)

Answer each query by printing YES if the servers can communicate and NO otherwise.

inputFormat

The input is read from stdin and has the following format:

1. The first line contains two integers n and m, where n is the number of servers and m is the number of direct links.
2. The next m lines each contain two integers u and v, representing a direct link between servers u and v (0-indexed).
3. The following line contains an integer q, the number of queries.
4. Each of the next q lines contains two integers a and b, representing a query asking whether server a can communicate with server b.

outputFormat

For each of the q queries, output a single line with either YES if server a and server b can communicate, or NO if they cannot.## sample

6 5
0 1
0 2
1 3
1 4
4 5
3
3 5
2 5
0 4

YES
YES
YES