P3174 [HAOI2009] Caterpillar

Thanks to @ScanfN for providing two sets of hack testdata.

For a tree, we can extract some path together with the edges incident to that path; it looks like a caterpillar. The more vertices it contains, the larger the caterpillar. For example, extracting part of the tree on the left (Figure $1$) yields the caterpillar on the right (Figure $2$). 

The first line contains two integers $N, M$, denoting the number of vertices and the number of edges in the tree. The next $M$ lines each contain two integers $a, b$, indicating that there is an edge between vertices $a$ and $b$ ($a, b \le N$). You may assume that no identical pair $(a, b)$ appears more than once.

Output a single integer on one line, representing the size of the largest caterpillar.

For $40\%$ of the testdata, $1\leq N \le 50000$. For $100\%$ of the testdata, $1\leq N \le 300000$. Translated by ChatGPT 5