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.Linq;
using System.Collections.Generic;

namespace CF2017_qual_B_C___3_Steps
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine(solver());
        }
        static long solver()
        {
            var NM = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            var N = NM[0]; var M = NM[1];

            var nodes = new Node[N + 1];
            for (int i = 0; i < N + 1; i++) nodes[i] = new Node();
            for (int i = 0; i < M; i++)
            {
                var ab = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
                nodes[ab[0]].connection.Add(ab[1]);
                nodes[ab[1]].connection.Add(ab[0]);
            }

            var queue = new Queue<Node>();
            queue.Enqueue(nodes[1]);
            var isSearch = new bool[N + 1];
            isSearch[1] = true;
            while (queue.Count > 0)
            {
                var current = queue.Dequeue();
                foreach (int n in current.connection)
                {
                    if (isSearch[n])
                    {
                        if (current.isBlack == nodes[n].isBlack) return (long)N * (long)(N - 1) / 2 - M;
                    }
                    else
                    {
                        isSearch[n] = true;
                        nodes[n].isBlack = !current.isBlack;
                        queue.Enqueue(nodes[n]);
                    }
                }
            }
            var black = nodes.Count(n => n.isBlack);
            return (long)black * (long)(N - black) - M;
        }

        class Node
        {
            public List<int> connection;
            public bool isBlack;
            public Node()
            {
                connection = new List<int>();
            }
        }
    }
}