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)

#include <stdio.h>
#include <stdlib.h>
#define NMAX 100000
struct node {
  int id;
  struct node *next;
};
struct node *list[NMAX];
void Insert(int a, int b);
int Dfs(int v, int c, int *color);
int main(void)
{
  int i, n, m, a, b, color[NMAX] = {0};
  long long int wb[2] = {0};
  scanf("%d %d", &n, &m);
  for (i = 0; i < n; i++) list[i] = NULL;
  for (i = 0; i < m; i++) {
    scanf("%d %d", &a, &b);
    Insert(a - 1, b - 1);
  }
  for (i = 0; i < n; i++) {
    if (color[i] == 0) {
      if (!Dfs(i, 1, color)) {
        printf("%lld\n", (long long int)(n - 1) * n / 2 - m);
        return 0;
      }
    }
  }
  for (i = 0; i < n; i++) {
     wb[(color[i]+1)/2]++;
     free(list[i]);
  }
  printf("%lld\n", wb[0] * wb[1] - m);
}

void Insert(int a, int b)
{
  struct node *p = (struct node*)malloc(sizeof(struct node));
  p->id = b;
  p->next = list[a];
  list[a] = p;
  p = (struct node*)malloc(sizeof(struct node));
  p->id = a;
  p->next = list[b];
  list[b] = p;
}

int Dfs(int v, int c, int *color)
{
  struct node *n;
  color[v] = c;
  for (n = list[v]; n != NULL; n = n->next) {
    if (color[n->id] == c) return 0;
    else if (color[n->id] == 0 && !Dfs(n->id, -c, color)) return 0;
  }
  return 1;
}