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
input = sys.stdin.buffer.readline

#sys.setrecursionlimit(10**9)
#from functools import lru_cache

def RD(): return sys.stdin.read()
def II(): return int(input())
def MI(): return map(int,input().split())
def MF(): return map(float,input().split())
def LI(): return list(map(int,input().split()))
def LF(): return list(map(float,input().split()))
def TI(): return tuple(map(int,input().split()))
# rstrip().decode()

from collections import deque

def main():
	n,m=MI()

	G=[[] for _ in range(n+1)]

	for _ in range(m):
		a,b=MI()
		G[a].append(b)
		G[b].append(a)
	#print(G)

	D=[-1]*(n+1)


	Q=deque()
	Q.append([1,0])

	#print(Q)

	f=0

	while Q:
		#print(Q)
		now,d=Q.popleft()
		D[now]=d
		for nx in G[now]:
			if D[nx]==-1:
				Q.append([nx,d+1])
			elif D[nx]%2!=d%2:
				continue
			else:
				f=1
				break


	if f==1:
		ans=(n*(n-1))//2+5
	else:
		ans=(n//2+n%2)*(n//2)

	ans-=m

	print(ans)

















if __name__ == "__main__":
	main()