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.io.*;
import java.util.*;

class Main {

	private static int[] color;
	private static int b = 0, w = 0;
	private static List<Integer>[] g;

	public static void main(String[] args) throws Exception {
		final Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int M = sc.nextInt();
		color = new int[N];
		g = new List[N];
		for (int i = 0; i < N; i++) {
			g[i] = new ArrayList<>();
		}

		for (int i = 0; i < M; i++) {
			int a = sc.nextInt() - 1;
			int b = sc.nextInt() - 1;
			g[a].add(b);
			g[b].add(a);
		}

		if (dfs(0, 1)) {
			System.out.println((long) N * (N - 1) / 2 - M);
		} else {
			System.out.println((long) b * w - M);
		}
	}

	static private boolean dfs(int v, int c) {
		if (color[v] != 0) {
			if (color[v] != c) return true;
			return false;
		}
		color[v] = c;
		int nc = 0;
		if (c == 1) {
			nc = 2;
			w++;
		} else {
			nc = 1;
			b++;
		}
		for (int next : g[v]) {
			if (dfs(next, nc)) return true;
		}
		return false;
	}
}