CF1268E Happy Cactus

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 $ .