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.Collections.Generic;
using static Assistant.Input;
using System.Linq;
using Assistant;

namespace Temp20200521
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = ReadInt;
            int M = ReadInt;

            List<int>[] edge = new List<int>[N].Select(x => new List<int>()).ToArray();
            for (int i = 0; i < M; i++)
            {
                int a = ReadInt - 1;
                int b = ReadInt - 1;
                edge[a].Add(b);
                edge[b].Add(a);
            }

            bool nibu = true;
            int[] color = new int[N];
            Queue<int> que = new Queue<int>();
            que.Enqueue(0);
            color[0] = 1;
            while (que.Count > 0 && nibu)
            {
                int now = que.Dequeue();

                foreach (var to in edge[now])
                {
                    if (color[to] == color[now])
                    {
                        nibu = false;
                        break;
                    }
                    if (color[to] == 0)
                    {
                        que.Enqueue(to);
                        color[to] = color[now] == 1 ? 2 : 1;
                    }
                }
            }

            int ans = 0;
            if (nibu)
            {
                ans = color.Count(x => x == 1) * color.Count(x => x == 2) - M;
            }
            else
            {
                ans = N * (N - 1) / 2 - M;
            }

            Console.WriteLine(ans);
        }


    }


}

namespace Assistant
{
    static class Input
    {
        static List<string> line = new List<string>();
        static int index = 0;
        static String ReadNext()
        {
            if (line.Count <= index) line.AddRange(Console.ReadLine().Split());
            return line[index++];
        }
        public static int ReadInt => int.Parse(ReadNext());
        public static long ReadLong => long.Parse(ReadNext());
        public static int[] ReadInts => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static long[] NextLongs => Console.ReadLine().Split().Select(long.Parse).ToArray();
    }
}