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 <iostream>
#include <iterator>
#include <algorithm>
#include <vector>
#include <queue>

using namespace std;
typedef long long LL;

class NODE{
  public:
  int color=0;
  vector<int> next;
};


int main(){
  int N,M;
  cin >> N >> M;
  vector<NODE> node(N);
  vector<int> _A(M);
  vector<int> _B(M);

  for(int i=0;i<M;i++){
	cin >> _A[i] >> _B[i];
	_A[i]--;
	_B[i]--;
	node[_A[i]].next.push_back(_B[i]);
	node[_B[i]].next.push_back(_A[i]);
  }
  
  queue<int> q;
  queue<int> q_color;
  int B=0;
  int W=0;
  q.push(0);
  q_color.push(1);
  while(!q.empty()){
	int pos=q.front();
	int color=q_color.front();
	q.pop();
	q_color.pop();
	if(node[pos].color==0){
	  node[pos].color=color;
	}else if(node[pos].color!=color){
	  cout << N*(N-1)/2-M << endl;
	  return 0;
	}
	if(color==1){
	  B++;
	}else{
	  W++;
	}
	for(int i=0;i<node[pos].next.size();i++){
	  int next=node[pos].next[i];
	  if(node[next].color==0){
		q.push(next);
		if(color==1){
		  q_color.push(2);
		}else{
		  q_color.push(1);
		}
	  }
	}
  }
  
  cout << B*W-M << endl;

  return 0;
}