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 System.Text;

static class Program
{
    static int[] Paint(int N, List<int>[] hands)
    {
        var colors = new int[N];
        var queue = new Queue<int>();
        colors[0] = 1;
        queue.Enqueue(0);
        while (queue.Count > 0)
        {
            int a = queue.Dequeue();
            foreach (int b in hands[a])
            {
                if (colors[b] == 0)
                {
                    colors[b] = -colors[a];
                    queue.Enqueue(b);
                }
                else if (colors[b] != -colors[a])
                {
                    return null;
                }
            }
        }
        return colors;
    }

    static long Solve(int N, int M, int[][] edges)
    {
        var hands = new List<int>[N];
        for (int i = 0; i < N; ++i) { hands[i] = new List<int>(); }
        foreach (var edge in edges)
        {
            int a = edge[0];
            int b = edge[1];
            hands[a].Add(b);
            hands[b].Add(a);
        }
        var colors = Paint(N, hands);
        if (colors != null)
        {
            int e = colors.Count(color => color == 1);
            int o = colors.Count(color => color == -1);
            return Math.BigMul(e, o) - M;
        }
        else
        {
            return Math.BigMul(N, N - 1) / 2 - M;
        }
    }

    static void Main(string[] args)
    {
        int[] V1 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int N = V1[0], M = V1[1];
        var edges = new int[M][];
        for (int i = 0; i < M; ++i)
        {
            edges[i] = Array.ConvertAll(Console.ReadLine().Split(), x => int.Parse(x) - 1);
        }
        Console.WriteLine(Solve(N, M, edges));
    }
}