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: Wrong Answer)

#include "bits/stdc++.h"
using namespace std;
#define ll long long int
#define rep(i,n) for( int i = 0; i < n; i++ )
#define rrep(i,n) for( int i = n; i >= 0; i-- )
#define REP(i,s,t) for( int i = s; i <= t; i++ )
#define RREP(i,s,t) for( int i = s; i >= t; i-- )
#define dump(x)  cerr << #x << " = " << (x) << endl;
#define INF 2000000000
#define mod 1000000007
#define INF2 1000000000000000000

vector<int> G[100010];

int color[100010];

// 頂点を1と-1で塗っていく
bool dfs(int v, int c) {
    color[v] = c;
    for (int i = 0; i < G[v].size(); i++) {
        // 隣接している頂点が同じ色ならfalse
        if (color[G[v][i]] == c) return false;
        // 隣接している頂点がまだ塗られていないなら-cで塗る
        if (color[G[v][i]] == 0 && !dfs(G[v][i], -c)) return false;
    }

    // すべての頂点を塗れたらtrue
    return true;

}
int main(void)
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N, M;
    cin >> N >> M;
    rep(i, M) {
        int s, t;
        cin >> s >> t;
        s--; t--;
        G[s].push_back(t);
        G[t].push_back(s);
    }
    if(dfs(0, 1)) {
        int k1 = 0, k2 = 0;
        rep(i, 100010) {
            if (color[i] == 1) k1++;
            else if (color[i] == -1) k2++;
        }
        cout << k1 * k2 - M << endl;
    } else {
        cout << N * (N - 1) / 2 - M << endl;
    }



    return 0;
}