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 Julia (0.5.0) (judge verdict: Wrong Answer)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)
function root(uf::Array{Int,1},x);s=x;while uf[s]>0;s=uf[s];end;s;end
same(uf::Array{Int,1},x,y)=root(uf,x)==root(uf,y)?true:false;
function unite(uf::Array{Int,1},x,y);l=root(uf,x);r=root(uf,y);if l!=r;if uf[l]<uf[r];uf[l]+=uf[r];uf[r]=l;else;uf[r]+=uf[l];uf[l]=r;end;end;end

function main()
	n,m = readline() |> split |> parseMap
	d = zeros(Int,n)
	e = Tuple{Int,Int}[(0,0) for i in 1:m]
	for i in 1:m
		a,b = readline() |> split |> parseMap
		d[a] += 1
		d[b] += 1
		e[i] = (a,b)
	end
	fo = 0
	fn = 0
	for i in 1:n
		if d[i]==1
			fo += 1
		elseif d[i]==n-1
			fn += 1
		end
	end
	if fo==n-1&&fn==1
		println(0)
	else
		if n%2==1
			println(div(n*(n-1),2)-m)
		else
			uf = -ones(Int,2*n)
			for i in 1:m
				unite(uf,e[i][1],e[i][2]+n)
				unite(uf,e[i][1]+n,e[i][2])
			end
			f = 0
			for i in 1:n
				if same(uf,i,n+i)
					f = 1
					break
				end
			end
			println(f==0?div(n*(n-1),2)-div((n>>1)*(n>>1+1),2)-m:div(n*(n-1),2)-m)
		end
	end
end

main()