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: Wrong Answer)

N, M = gets.split.map(&:to_i)
edge = []
M.times do |i|
  edge[i] = gets.split.map(&:to_i)
  edge[i][0] -= 1
  edge[i][1] -= 1
end

network = Array.new(N)
sets = (0...N).to_a
sets_r = (0...N).to_a
color = Array.new(N)
parity = false
edge.each do |x|
  # puts(" " + x.join(","))
  if color[x[0]].nil? && color[x[1]].nil?
    # puts(" " + x.join(","))
    color[x[0]] = 1
    color[x[1]] = -1
  elsif color[x[0]].nil? || color[x[1]].nil?
    # puts(" " + x.join(","))
    if color[x[0]].nil?
      color[x[0]] = -color[x[1]]
    else
      color[x[1]] = -color[x[0]]
    end
  elsif color[x[0]] * color[x[1]] == 1
    parity = true
  end
end

# N.times do |i|
#   network[i][1] = []
#   network[i][0].each do |e|
#     network[e][0].each do |ind|
#       network[i][1] << ind if ind != i
#     end
#   end
#   network[i][1].uniq
# end

# # p network[0]
# # p network[network[0][1][0]]
# N.times do |i|
#   network[i][2] = []
#   network[i][1].each do |e|
#     network[e][0].each do |ind|
#       network[i][2] << ind if ind != i
#     end
#   end
#   network[i][2].uniq
# end

# ret = 0
# flag = true
# p network[0]
# while flag
#   flag = false
#   N.times do |i|
#     network[i][2].each do |e|
#       network[i][2].delete(e)
#       network[e][2].delete(i)
#       next if network[i][0].include?(e)
#       # puts("e: " + [i, e].join(" "))
#       ret += 1
#       network[i][0] << e
#       network[e][0] << i
#       flag = true
#       network[e][1].each do |ind|
#         network[i][2] << ind if ind != i
#       end
#       network[i][2].uniq
#       network[i][1].each do |ind|
#         network[e][2] << ind if ind != e
#       end
#       network[2][2].uniq
#     end
#   end
# end
# p parity
if parity
  puts N*(N-1)/2 - M
else
  if N == 2
    puts 0
  elsif N == 3
    puts 0
  elsif N % 2 == 0
    puts(N/2 * (N/2 - 1) - M)
  else
    puts(N/2 * (N/2 - 1) + 2 - M)
  end
end