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 Python (3.4.3) (judge verdict: Wrong Answer)

import sys
sys.setrecursionlimit(10**6)
n,m=map(int,input().split())
s=[[]for i in range(n+1)]
c=[0]*(n+1)
for i in range(m):
    a,b=map(int,input().split())
    s[a].append(b)
    s[b].append(a)
def dfs(v,t):
    c[v]=t
    # print('start :'+str(c))
    for i in s[v]:
        if c[i]==t:
            return False
        if c[i]==0:
            dfs(i,-t)
            # return False
    else:
        return True
if dfs(1,1):
    q=c.count(1)
    print((n-q)*q-m)
else:
    print((n*(n-1)//2)-m)