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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {
    int n, m;
    ArrayList<ArrayList<Integer>> es;
    int[] cs;

    public static void main(String[] args) {
        Main m = new Main();
        m.read();
        m.solve();
    }

    private void read() {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        m = sc.nextInt();
        es = new ArrayList<>(n);
        cs = new int[n];
        for (int i = 0; i < n; i++) {
            es.add(new ArrayList<>());
        }
        for (int i = 0; i < m; i++) {
            int a = sc.nextInt() - 1;
            int b = sc.nextInt() - 1;
            es.get(a).add(b);
            es.get(b).add(a);
        }
    }

    private void solve() {
        // judge
        long ans;
        if (check(0, 1)) {
            int b = 0;
            for (int c: cs)
                if (c == 1) b++;
            ans = (long) b * (n - b) - m;
        }
        else {
            ans = (long) n * (n - 1) / 2L;
            ans -= m;
        }
        System.out.println(ans);
    }

    private boolean check(int v, int c) {
        if (cs[v] != 0)
            return c == cs[v];
        cs[v] = c;
        boolean ans = true;
        for (int nxt: es.get(v)) {
            ans &= check(nxt, -c);
        }
        return ans;
    }

}