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: Runtime Error)

import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)

N,M = map(int, input().split())
AB = [[int(x) for x in input().split()] for _ in range(M)]

graph = [[] for _ in range(N+1)]
for a, b in AB:
	graph[a].append(b)
	graph[b].append(a)

color = [None] * (N+1)
color[1] = 0
q = [1]
while q:
	x = q.pop()
	for y in graph[x]:
		if color[y] is not None:
			color[y] = 1-color[x]
			q.append(y)

bl = all(color[a] != color[b] for a, b in AB)

if bl :
	x = sum(color[1:])
	y = N - x
	ans = x * y - M
else:
	ans - N*(N-1) // 2 - M
print(ans)