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>
#define repd(i, a, b) for (int i = (a); i < (b); i++)
#define rep(i, n) repd(i, 0, n)
#define INF 2e9
#define ALL(v) v.begin(), v.end()
using namespace std;
typedef long long ll;
template <class T>
inline bool chmin(T &a, T b)
{
    if (a > b)
    {
        a = b;
        return true;
    }
    return false;
}
template <class T>
inline bool chmax(T &a, T b)
{
    if (a < b)
    {
        a = b;
        return true;
    }
    return false;
}

vector<int> color;
vector<vector<int>> G;

bool dfs(int v, int c)
{
    color[v] = c;
    rep(i, G[v].size())
    {
        if (color[G[v][i]] == c)
        {
            return false;
        }
        if (color[G[v][i]] == 0 && !dfs(G[v][i], -c))
        {
            return false;
        }
    }

    return true;
}

int main()
{
    int N, M;
    cin >> N >> M;

    G = vector<vector<int>>(N);
    color = vector<int>(N, 0);

    rep(i, M)
    {
        int s, t;
        cin >> s >> t;
        G[s - 1].push_back(t - 1);
        G[t - 1].push_back(s - 1);
    }

    bool flag = true;
    rep(i, N)
    {
        if (color[i] == 0)
        {
            flag = dfs(i, 1);
            if (!flag)
            {
                break;
            }
        }
    }

    int B = 0, W = 0;
    if (flag)
    {
        rep(i, N)
        {
            if (color[i] == 1)
            {
                B++;
            }
            else
            {
                W++;
            }
        }
        cout << B * W - M << endl;
    }
    else
    {
        cout << N * (N - 1) / 2 - M << endl;
    }

    return 0;
}