POI 2008, BLO

Problem Description

Given an undirected connected graph with $n$ vertices and $m$ edges, with no multiple edges or self-loops. For each vertex, after deleting all its incident edges, how many pairs of vertices can no longer reach each other? The pairs are ordered, so $(u, v)$ and $(v, u)$ are counted twice.

Input Format

The first line contains two integers $n, m\ (1 \le n \le 10^5,\ 1 \le m \le 5 \times 10^5)$.

The next $m$ lines each contain two integers $u, v$, denoting an undirected edge.

Output Format

$n$ lines, each containing one integer: the answer for the corresponding vertex.

Sample Input

5 5
1 2
2 3
1 3
3 4
4 5

Sample Output

8
8
16
14
8