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;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		HashSet<int>[] E = new HashSet<int>[N];
		for(int i=0;i<N;i++) E[i] = new HashSet<int>();
		for(int i=0;i<M;i++){
			E[A[i]].Add(B[i]);
			E[B[i]].Add(A[i]);
		}
		
		for(int i=0;i<M;i++){
			foreach(var na in E[A[i]]){
				if(E[B[i]].Contains(na)){
					var tot = (long) N * (long)(N - 1) / 2;
					Console.WriteLine(tot - M);
					return;
				}
			}
			foreach(var nb in E[B[i]]){
				if(E[A[i]].Contains(nb)){
					var tot = (long) N * (long)(N - 1) / 2;
					Console.WriteLine(tot - M);
					return;
				}
			}
		}
		
		long tot0 = 0;
		for(long i=0;i<N;i++){
			tot0 += (i+1)/2;
		}
		Console.WriteLine(tot0 - M);
		
		
		
	}
	int N,M;
	int[] A,B;
	public Sol(){
		var d = ria();
		N = d[0]; M = d[1];
		A = new int[M];
		B = new int[M];
		for(int i=0;i<M;i++){
			d = ria();
			A[i] = d[0] - 1;
			B[i] = d[1] -1;
		}
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}