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: Accepted)

#include <iostream>
#include <vector>
#include <cstdio>
#include <algorithm>
#include <utility>
#include <string>
#include <cmath>
#include <set>
#include <functional>
#include <map>
#include <queue>
#include <cstring>
#include <stack>
#include <iomanip>
#include <climits>
#include <numeric>
#include <cassert>
#include <unordered_map>
using namespace std;
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define show(x) cout << #x << " = " << x << endl;
typedef long long ll;
typedef pair<int,int> pii;
#include <iostream>
#include <vector>
#include <cstdio>
using namespace std;
vector<int> G[100005];
int V;

int color[100005];

bool dfs(int v, int c){
    color[v] = c;
    for(int i = 0; i < G[v].size(); i++){
        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(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    ll n,m;
    cin >> n >> m;
    int a,b;
    rep(i,m){
        cin >> a >> b;
        a--,b--;
        G[a].push_back(b);
        G[b].push_back(a);
    }
    if(dfs(0,1)){
        ll hoge = 0;
        rep(i,n){
            if(color[i]==1)hoge++;
        }
        cout << hoge*(n-hoge) -m << endl;
    }else{
        cout << n*(n-1)/2-m << endl;
    }
    return 0;
}