E. Happy Cactus
dp
You are given a cactus graph, in this graph each edge lies on at most one simple cycle.It is given as \(m\) edges \(a_i, b_i\), weight of \(i\)-th edge is \(i\).Let's call a path in cactus increasing if the weights of edges on this path are increasing.Let's call a pair of vertices \((u,v)\) happy if there exists an increasing path that starts in \(u\) and ends in \(v\).For each vertex \(u\) find the number of other vertices \(v\), such that pair \((u,v)\) is happy.
The first line of input contains two integers \(n,m\) (\(1 \leq n, m \leq 500\,000\)): the number of vertices and edges in the given cactus.The next \(m\) lines contain a description of cactus edges, \(i\)-th of them contain two integers \(a_i, b_i\) (\(1 \leq a_i, b_i \leq n, a_i \neq b_i\)).It is guaranteed that there are no multiple edges and the graph is connected.
Print \(n\) integers, required values for vertices \(1,2,\ldots,n\).