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++ (GCC 5.4.1) (judge verdict: Accepted)

// luogu-judger-enable-o2
#include<bits/stdc++.h>
#define maxn 100005
#define ll long long
using namespace std;

int head[maxn],cnt,vis[maxn];ll cnt1,cnt2,n,m;

struct edge{
	int to,nxt;
}e[maxn<<1];

void add(int u,int v){
	e[++cnt]=(edge){v,head[u]};
	head[u]=cnt;
}

void dfs(int u,int fa,int col){
	if(!vis[u]) vis[u]=col;
	else {
		if(vis[u]!=col){
			printf("%lld",(n-1)*n/2-m);
			exit(0);
		}
		return ;
	}
	col&1?cnt1++:cnt2++;
	for(int i=head[u];i;i=e[i].nxt){
		int v=e[i].to;
		if(v==fa) continue;
		dfs(v,u,(col&1)+1);
	}
}

int main(){
	scanf("%lld%lld",&n,&m);
	for(int i=1,u,v;i<=m;i++){
		scanf("%d%d",&u,&v);
		add(u,v);add(v,u);
	}
	dfs(1,0,1);
	printf("%lld",cnt1*cnt2-m);
}