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: Accepted)

n,m=gets.split.map &:to_i
a=Array.new(n)
b=Array.new(n).map{[]}
m.times do
  x,y=gets.split.map &:to_i
  b[y-1]<< x-1
  b[x-1]<< y-1
end
t=[0]
a[0]=0
even=1
odd=0
j=false
loop do
  break if t==[]
  g=t.pop
  c=a[g]+1
  b[g].each do |e|
    if a[e]
      if (a[e]-c)%2!=0
        j=true
      end
    else
      t<< e
      a[e]=c
      c.even? ? even+=1 : odd+=1
    end
  end
end
if j
  p n*(n-1)/2 - m
else
  p even*odd - m
end