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 Lua (5.3.2) (judge verdict: Accepted)

local n, m = io.read("*n", "*n")
local color = {}
local edge = {}
for i = 1, n do
  color[i] = 0
  edge[i] = {}
end
local tasks = {}
do
  local a, b = io.read("*n", "*n")
  color[a] = 1
  color[b] = 2
  tasks[1] = a
  tasks[2] = b
  table.insert(edge[a], b)
  table.insert(edge[b], a)
end
for i = 2, m do
  local a, b = io.read("*n", "*n")
  table.insert(edge[a], b)
  table.insert(edge[b], a)
end
local allsame = false
for itask = 1, n do
  local src = tasks[itask]
  for j = 1, #edge[src] do
    local dst = edge[src][j]
    if color[dst] == 0 then
      color[dst] = 3 - color[src]
      table.insert(tasks, dst)
    elseif color[dst] == color[src] then
      allsame = true
      break
    end
  end
  if allsame then break end
end
if allsame then
  print(n * (n - 1) // 2 - m)
else
  local cnt1, cnt2 = 0, 0
  for i = 1, n do
    if color[i] == 1 then
      cnt1 = cnt1 + 1
    else
      cnt2 = cnt2 + 1
    end
  end
  print(cnt1 * cnt2 - m)
end