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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

n,m = map(int,readline().split())
data = list(map(int,read().split()))

links = [[] for _ in range(n+1)]
it = iter(data)
for a,b in zip(it,it):
    links[a].append(b)
    links[b].append(a)

color = [-1] * (n+1)
color[1] = 0
stack = [1]
while(stack):
    i = stack.pop()
    ci = color[i]
    for j in links[i]:
        if(color[j] == -1):
            color[j] = 1-ci
            stack.append(j)
        else:
            if(color[j]==ci):
                ans = (n*(n-1))//2 - m
                print(ans)
                exit()

n0 = color.count(0)
n1 = color.count(0)
ans = n0*n1 - m
print(ans)