Lethargic Lumen

Pogi spends his days watching undirected graphs without cycles.

Pogi wants to turn one such graph with $n$ nodes and $m$ edges into a tree. He adds some edges, and he wants the resulting tree to have the smallest possible diameter.

A tree on $n$ nodes is a connected undirected graph with $n$ nodes and no cycles.

The diameter of a tree is the maximum distance between any two nodes in it.

Help Pogi, since he is a good person and does not want trouble.

The first line contains natural numbers $n$ ($1 \le n \le 100\,000$) and $m$ ($0 \le m \le m - 1$) from the problem text.

The next $n$ lines each contain two natural numbers that describe an edge of the initial graph.

The node labels are integers from $0$ to $n - 1$.

Print the smallest possible diameter of the tree on a single line.