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: Accepted)

#![allow(non_snake_case,unused_imports)]
use std::io::Read;
use std::cmp::max;
use std::cmp::min;
use std::str::FromStr;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::BinaryHeap;

fn bfs_dist(N:usize,E:&Vec<Vec<usize>>,start:usize) -> Vec<isize>{
    let mut D = (0..N).map(|_| -1).collect::<Vec<_>>();
    D[start] = 0;
    let mut q = vec![start];
    while q.len()>0{
        let mut qq = Vec::new();
        for &i in &q{
            for &j in &E[i]{
                if D[j]!=-1{continue;}
                D[j] = D[i]+1;
                qq.push(j);
            }
        }
        q = qq;
    }
    D
}

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let N = iter.next().unwrap().parse::<usize>().unwrap();
    let M = iter.next().unwrap().parse::<usize>().unwrap();
    let AB = (0..M).map(|_| (
        iter.next().unwrap().parse::<usize>().unwrap()-1,
        iter.next().unwrap().parse::<usize>().unwrap()-1
    )).collect::<Vec<_>>();

    let mut E = (0..N).map(|_| Vec::new()).collect::<Vec<_>>();
    for &(a,b) in &AB{
        E[a].push(b);
        E[b].push(a);
    }
    let D = bfs_dist(N,&E,0);
    let mut is_bipartite = true;
    for &(a,b) in &AB{
        is_bipartite = (D[a]^D[b])&1==1;
        if !is_bipartite {break;}
    }
    if is_bipartite{
        let mut n0 = 0;
        for &d in &D{
            n0 += (d%2) as usize;
        }
        let n1 = N-n0;
        println!("{}",n0*n1-M);

    } else {
        println!("{}",N*(N-1)/2-M);
    }
}