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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
using Pair = System.Tuple<int, int>;
using Edge = System.Tuple<int, int, long>;
//using Debug;
//using static System.Globalization.CultureInfo;

class Program
{
    static void Main(string[] args)
    {
        var nm = Input.ar;
        var adj = Enumerable.Repeat(0, nm[0]).Select(_ => new List<int>()).ToArray();
        for(var i = 0; i < nm[1]; i++)
        {
            var inp = Input.ar;
            adj[inp[0] - 1].Add(inp[1] - 1);
            adj[inp[1] - 1].Add(inp[0] - 1);
        }
        var color = new int[nm[0]];
        if (isBip(color, adj, 0, 1))
            WriteLine((long)color.Count(v => v == 1) * color.Count(v => v == 2) - nm[1]);
        else WriteLine((long)nm[0] * (nm[0] - 1) / 2 - nm[1]);
    }
    private static bool isBip(int[] color,List<int>[] adj,int index,int c)
    {
        color[index] = c;
        var r = true;
        foreach (var ad in adj[index])
            if (r && color[ad] == 0)
                r = isBip(color, adj, ad, 3 - c);
            else r &= color[ad] == 3 - c;
        return r;
    }
}

public class Input
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public static char[][] gred(int h) 
        => Enumerable.Repeat(0, h).Select(v => read.ToCharArray()).ToArray();
    public static int[][] twodim(int num)
        => Enumerable.Repeat(0, num).Select(v => ar).ToArray();
    public static long[][] twodimL(int num)
        => Enumerable.Repeat(0, num).Select(v => arL).ToArray();
    public const long Inf = (long)1e18/2;
    public const double eps = 1e-6;
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}