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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;//リストを使う
class Program
{

static string[] input = Console.ReadLine().Split(' ');
static int n = int.Parse(input[0]);
static int m = int.Parse(input[1]);
static int[] result = new int[n];//頂点0を１、隣接頂点を2と、交互に塗る。
static List<int>[] nextList = new List<int>[n];//隣接リスト
static bool twoGraph = true;//２部グラフならtrue

	 static void Main()
  {
    for(int i = 0; i < n; i++) nextList[i] = new List<int>();//リストの宣言
    for(int i = 0; i < m; i++)
    {
      int[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);//１行ごとに受け取る
      nextList[nums[0]-1].Add(nums[1]-1);//隣接リストへ追加。
      nextList[nums[1]-1].Add(nums[0]-1);
    }
        
          result[0] = 1;
          Spread(0);//頂点0から色を広げる

         if(twoGraph) //２部グラフのとき
         {
            int whiteNum = 0;//頂点0と同じ色の頂点数
            for (int i = 0; i < n; i++)
            {
              if(result[i] == 1) whiteNum++;
            }
            Console.WriteLine(whiteNum*(n-whiteNum)-m);
         }
         else Console.WriteLine(n*(n-1)/2-m);//２部グラフでないとき
  }

   static void Spread(int vertex)//色を広げる
  {
    int color = result[vertex];//現在の頂点の色
  
    for(int i = 0; i < nextList[vertex].Count(); i++)
    {
        if(result[nextList[vertex][i]] == 0)
        {
          result[nextList[vertex][i]] = 3 - color;//隣接頂点は別の色で塗る
          Spread(nextList[vertex][i]);//色を広げる
        }
        else if(result[nextList[vertex][i]] == color) twoGraph = false;//色の矛盾がある
    }
  }
}