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)
edges = Array.new(n+1).map{[]}
p = Array.new(n,0)
used = Array.new(n,true)
ans = true

m.times {
  a,b = gets.split.map{|i|i.to_i-1}
  edges[a] << b
  edges[b] << a
}

used[0] = false
q = [0]
while q.any?
  f = q.shift
  edges[f].each { |i|
    if used[i]
      used[i] = false
      p[i] = 1-p[f]
      q.push(i)
    elsif p[i] == p[f]
      ans = false
    end
  }
end

if ans
  c = p.count(0)
  puts c*(n-c)-m
else
  puts (n*(n-1))/2-m
end