Villagers Connectivity Check

Given n villagers and q friendship pairs, determine whether all villagers are connected, either directly or indirectly. Two villagers are said to be connected if there exists a sequence of friendships connecting them. In other words, the friendship network forms a single connected component.

You are given a graph with n nodes and q edges. The connectivity condition can be expressed in \( \text{latex} \) as:

\( \forall v \in \{1, 2, \dots, n\}, \; \exists\; \text{a path from } 1 \text{ to } v \).

If all villagers are interconnected, print YES; otherwise, print NO.

inputFormat

The first line of input contains two integers n and q where n is the number of villagers and q is the number of friendship pairs.

Each of the next q lines contains two integers u and v representing a friendship between villagers u and v.

Note: The villagers are numbered from 1 to n.

outputFormat

Output a single line containing YES if all villagers are connected, otherwise output NO.

5 4
1 2
2 3
4 5
3 4

YES