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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<cstdio>
struct edge{
	int to,next;
}e[1008611];
int fa[1008611],k=1,color[1008611],head[1008611];
int bw[3];
inline void addedge(int u,int v){
	e[k]=(edge){v,head[u]};
	head[u]=k++;
}
inline void add(int u,int v){
	addedge(u,v); addedge(v,u);
}
bool tu(int p){
	for(int i=head[p];i!=0;i=e[i].next){
        int v=e[i].to;
        if(color[v]==color[p]) return false;
        if(color[v]==0){
        	color[v]=3-color[p];
        	bw[color[v]]++;
        	if(!tu(v)) return false;
		}
    }
    return true;
}
int main(){
	int n,m;
	scanf("%d%d",&n,&m);
	for(int i=0;i<m;i++){
		int a,b;
		scanf("%d%d",&a,&b);
		add(a,b);
	}
	color[1]=1;
	bw[1]++;
	if(tu(1)) printf("%d",bw[1]*bw[2]-m);
	else printf("%d",n*(n-1)/2-m);
}