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 System.Linq;
class Program{
	static bool?[] h;
	static int ans=0;
	static List<int>[] li;
	static void Main(){
		int[] s=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
		li=new List<int>[s[0]+1];
		h=new bool?[s[0]+1];
		for(int i=1;i<=s[0];i++){li[i]=new List<int>();}
		for(int i=0;i<s[1];i++){
			int[] q=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
			li[q[0]].Add(q[1]);
			li[q[1]].Add(q[0]);
		}
		fu(1,true);
		if(ans==1){ans=s[0]*(s[0]-1)/2;}
		else{
			for(int i=1;i<=s[0];i++){
				if(h[i]==true){ans++;}
			}
			ans=ans*(s[0]-ans);
		}
		Console.WriteLine(ans-s[1]);
	}
	static void fu(int a,bool b){
		h[a]=b;
		for(int i=0;i<li[a].Count&&ans==0;i++){
			if(h[li[a][i]]==null){fu(li[a][i],!b);}
			else if(h[li[a][i]]==b){
				ans=1;
				break;
			}
		}
	}
}