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++14 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include<cstdio>
#include<iostream>
#include<vector>
#include<cstring>
using namespace std;
vector<int > v[100001];
int p[100001];
int n,m;
bool flag=true;
int s[2]={0};
void dfs(int pos,int t)
{
	if(p[pos]==-1)
	{
    	p[pos]=t;
    	s[t]++;
	}
	else if(p[pos]!=-1&&p[pos]==t)
	return ;
	else if(p[pos]!=-1&&p[pos]!=t)
	{
		flag=false;
		return;
	}
	if(!flag) return;
	for(int i=0;i<v[pos].size();i++)
	{
		dfs(v[pos][i],1-t);
	}
}
int main()
{
	cin>>n>>m;
	memset(p,-1,sizeof(p));
	for(int i=1;i<=m;i++)
	{
		int x,y;
		cin>>x>>y;
		v[x].push_back(y);
		v[y].push_back(x);
	}
    dfs(1,0);	
    int sum=0;
    if(flag)
    {
		for(int i=1;i<=n;i++)
		{
			sum+=s[1-p[i]]-v[i].size();
		}
		cout<<sum/2<<endl;
	}
	else {
		for(int i=1;i<=n;i++)
		sum+=n-v[i].size()-1;
		cout<<sum/2<<endl;
	}
}