Problem:
Score : 500 points

Problem Statement

Rng has a connected undirected graph with N vertices.
Currently, there are M edges in the graph, and the i-th edge connects Vertices A_i and B_i.

Rng will add new edges to the graph by repeating the following operation:

Operation: Choose u and v (u \neq v) such that Vertex v can be reached by traversing exactly three edges from Vertex u, and add an edge connecting Vertices u and v. It is not allowed to add an edge if there is already an edge connecting Vertices u and v.

Find the maximum possible number of edges that can be added.

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq A_i,B_i \leq N

The graph has no self-loops or multiple edges.

The graph is connected.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
:
A_M B_M

Output

Find the maximum possible number of edges that can be added.

Sample Input 1

6 5
1 2
2 3
3 4
4 5
5 6

Sample Output 1

4

If we add edges as shown below, four edges can be added, and no more.

Sample Input 2

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

Sample Output 2

5

Five edges can be added, for example, as follows:

Add an edge connecting Vertex 5 and Vertex 3.

Add an edge connecting Vertex 5 and Vertex 2.

Add an edge connecting Vertex 4 and Vertex 1.

Add an edge connecting Vertex 4 and Vertex 2.

Add an edge connecting Vertex 4 and Vertex 3.

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

require 'set'
n,m=gets.split(" ").map(&:to_i)
@edge=Array.new(n){[]}
m.times{
    a,b=gets.split(" ").map{|k|k.to_i-1}
    @edge[a].<<b
    @edge[b].<<a
}
$id=Array.new(n,-1)
def check i,k
    $id[i]=k
    k+=1
    for j in @edge[i] do
        if $id[j]==-1 then
            check(j,k)
        elsif $id[j]&1==$id[i]&1 then
            return true
        end
    end
    return false
end
if check(0,0) then
    puts n*(n-1)/2-m
else
    blk=0
    whi=0
    for i in 0...n do
        if $id[i]%2==0 then
            blk+=1
        else whi+=1
        end
    end
    ret=0
    for i in 0...n do
        if $id[i]&1 then
            ret+=whi-@edge[i].length
        else    ret+=blk-@edge[i].length
        end
    end
    puts ret/2
end