Graph Connectivity Queries

You are given an undirected graph with n intersections (nodes) and m roads (edges). Each road connects two intersections. After constructing the graph, you are given q queries. In each query, you are given two intersections, and you must determine whether there is a path connecting them.

The problem can be formalized as follows: Let \(G=(V,E)\) be an undirected graph where \(|V|=n\) and \(|E|=m\). For each query \((a,b)\), determine if there exists a path from \(a\) to \(b\).

Input constraints:
\(1 \leq n \leq 10^5\), \(0 \leq m \leq 10^5\), and \(1 \leq q \leq 10^5\).

All nodes are numbered from 1 to n. Use depth-first search (DFS) or union-find (disjoint-set union) to solve the problem efficiently.

inputFormat

The input is given via standard input (stdin) in the following format:

n m
u1 v1
u2 v2
... (m lines)
q
a1 b1
a2 b2
... (q lines)

Here, the first line contains two integers, n and m. Then follow m lines each containing two integers u and v indicating there is a road between intersections u and v. The next line contains the integer q, the number of queries, followed by q lines with two integers each representing the query intersections.

outputFormat

For each query, output a single line containing YES if there is a path between the two intersections, or NO if not.

## sample

5 4
1 2
2 3
3 4
4 5
3
1 5
2 4
5 1

YES
YES
YES

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