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.IO;
using System.Linq;
using System.Text;
using System.Collections.Generic;
using System.Diagnostics;
using Enu = System.Linq.Enumerable;

public class Program
{
    public void Solve()
    {
        int N = Reader.Int(), M = Reader.Int();
        var graph = new BipartiteGraph(N);
        for (int i = 0; i < M; i++)
            graph.AddEdge(Reader.Int() - 1, Reader.Int() - 1);
        if (graph.IsBipartite()) Console.WriteLine((long)graph.A.Count * graph.B.Count - M);
        else Console.WriteLine((long)N * (N - 1) / 2 - M);
    }
}

public class BipartiteGraph
{
    public List<int> A = new List<int>(), B = new List<int>();
    readonly int N;
    readonly List<int>[] E;

    public BipartiteGraph(int N)
    {
        this.N = N;
        E = new List<int>[N];
        for (int i = 0; i < N; i++) E[i] = new List<int>();
    }

    public void AddEdge(int a, int b) { E[a].Add(b); E[b].Add(a); }

    public bool IsBipartite()
    {
        var mark = new int[N];
        Func<int, int, bool> DFS = null;
        DFS = (v, sign) =>
        {
            mark[v] = sign;
            if (sign == 1) A.Add(v);
            else B.Add(v);
            foreach (int next in E[v])
                if (mark[next] == mark[v]) return false;
                else if (mark[next] == 0 && !DFS(next, -sign)) return false;
            return true;
        };
        for (int i = 0; i < N; i++)
            if (mark[i] == 0 && !DFS(i, 1)) return false;
        return true;
        
        //var mark = new int[N];
        //var que = new Queue<int>();
        //for (int i = 0; i < N; i++)
        //    if (mark[i] == 0)
        //        for (que.Enqueue(i); que.Count > 0; )
        //        {
        //            int m = que.Dequeue(), v = m >> 1, parity = m & 1;
        //            mark[v] = (parity << 1) - 1;
        //            if (mark[v] == 1) A.Add(v);
        //            else B.Add(v);
        //            foreach (int next in E[v])
        //                if (mark[next] == mark[v]) return false;
        //                else if (mark[next] == 0) que.Enqueue(next << 1 | parity ^ 1);
        //        }
        //return true;
    }
}


class Entry { static void Main() { new Program().Solve(); } }
class Reader
{
    static TextReader reader = Console.In;
    static readonly char[] separator = { ' ' };
    static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries;
    static string[] A = new string[0];
    static int i;
    static void Init() { Dispose(); A = new string[0]; }
    public static void Set(TextReader r) { Init(); reader = r; }
    public static void Set(string file) { Init(); reader = new StreamReader(file); }
    public static bool HasNext() { return CheckNext(); }
    public static string String() { return Next(); }
    public static int Int() { return int.Parse(Next()); }
    public static long Long() { return long.Parse(Next()); }
    public static double Double() { return double.Parse(Next()); }
    public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); }
    public static int[] IntArray(int N) { return Range(N, Int); }
    public static int[][] IntTable(int H) { return Range(H, IntLine); }
    public static string[] StringArray(int N) { return Range(N, Next); }
    public static string[][] StringTable(int N) { return Range(N, () => Split(Line())); }
    public static string Line() { return reader.ReadLine().Trim(); }
    public static T[] Range<T>(int N, Func<T> f) { var r = new T[N]; for (int i = 0; i < N; r[i++] = f()) ; return r; }
    public static void Dispose() { reader.Dispose(); }
    static string[] Split(string s) { return s.Split(separator, op); }
    static string Next() { CheckNext(); return A[i++]; }
    static bool CheckNext()
    {
        if (i < A.Length) return true;
        string line = reader.ReadLine();
        if (line == null) return false;
        if (line == "") return CheckNext();
        A = Split(line);
        i = 0;
        return true;
    }
}