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 Rust (1.15.1) (judge verdict: Time Limit Exceeded)

#[warn(unused_imports)]
use std::io::*;
use std::str::FromStr;
use std::cmp;

#[warn(unused_variables)]

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn dfs(n: usize, graph: &Vec<Vec<i64>>, color: &mut Vec<i64>) -> bool {
    let mut stack: Vec<usize> = Vec::new();
    stack.push(1);
    color[1] = 1;
    while !stack.is_empty() {
        let v = stack.pop().unwrap();
        for i in 1..n+1 {
            if graph[v][i] == 1 {
                if color[i] == 0 {
                    stack.push(i);
                    color[i] = -color[v]
                } else if color[i] == color[v] {
                    return false;
                }
            }
        }
    }
    //println!("{:?}", color);
    return true;
}

fn solve(graph: &mut Vec<Vec<i64>>, n: usize, m: usize) {
    let mut color = vec![0; n+1];
    let bipartite: bool = dfs(n, &graph, &mut color);
    if bipartite {
        let l: Vec<i64> = color.into_iter().map(|c| if c > 0 { c } else { 0 }).collect();
        let k = l.iter().fold(0, |acc, x| acc + x);
        let n = n as i64;
        let m = m as i64;
        println!("{:?}", k * (n - k) - m);
    } else {
        println!("{}", n * (n-1) / 2 - m);
    }
}

fn main() {
    let n = read::<usize>(); // 頂点数
    let m = read::<usize>(); // 辺の数
    let mut graph: Vec<Vec<i64>> = vec![vec![0; n+1]; n+1];
    for _ in 0..m {
        let a = read::<usize>();
        let b = read::<usize>();
        graph[a][b] = 1;
        graph[b][a] = 1;
    }
    solve(&mut graph, n, m);
}