E. Happy Cactustime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputPrint n integers, required values for vertices 1,2,\ldots,n.ExamplesInput
3 3
1 2
2 3
3 1
Output
2 2 2 
Input
5 4
1 2
2 3
3 4
4 5
Output
4 4 3 2 1 

3 3
1 2
2 3
3 1

2 2 2  
['dp', '*3400']