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)

/**
*
* Author: Mouhanad
* Lang: GNU C++14
*
**/
#include<bits/stdc++.h>
using namespace std;

#define F first
#define S second
#define ii pair < int , int >
#define LS pair < ll , string >
typedef long long ll;
const int inf = 1<<30;
const int N =100100;
int n , a[N] , m ;

int main ( ){
 scanf("%d %d",&n,&m);
 int x , y ;
 for ( int i =0  ; i < m ;i++ ) {
    scanf("%d %d",&x,&y);
 }
 if ( n == 2 || n == 3 ){
    printf("0");
    return 0;
 }
   ll ANS = 0 ;
  if ( n&1 ){
  ll deg = n-1 ;
    ANS += (1LL*(deg)*n)/2LL ;
  }else {
    ll deg = n/2LL ;
    ANS += (1LL*(deg)*n)/2LL ;
  }
  printf("%lld",ANS-m);
return 0 ;
}