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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include"bits/stdc++.h"
using namespace std;

#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define REP(i, n) for (int i = 1; i <= (int)(n); i++)
#define all(v) v.begin(), v.end()
using ll = long long;

bool dfs(vector<vector<int>>& node,vector<int> &color, int v, int cor) {
	color[v] = cor;
	for (auto next_v : node[v]) {

		if (color[next_v] != -1) {
			if (color[next_v] == cor)return false;
			continue;
		}
		if (!dfs(node, color, next_v, !cor))return false;
	}
	return true;
}

int main() {
	int n, m;
	map<int, int>mp;
	int a, b;
	a = b = n = m = 0;
	cin >> n >> m;
	vector<vector<int>>node(n);
	vector<int>color(n, -1);
	rep(i, m) {
		cin >> a >> b;
		a--, b--;
		node[a].push_back(b);
		node[b].push_back(a);
	}

	if (!dfs(node,color, 0, 0)) cout << ((n * (n - 1)) / 2) - m << endl;
	else {
		for (int c : color) {
			mp[c]++;
		}
		cout << mp[0] * mp[1] - m << endl;
	}
	return 0;
}