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;
typedef long long LL;
const int MaxN = 100003;
int n,m;
vector<int> e[MaxN];
int color[MaxN];
bool paint(int x,int c) {
    color[x]=c;
    int nxt=3-c;
    for (auto i:e[x]) {
        if (!color[i]) if (!paint(i,nxt)) return false;
        if (color[i]!=c) return false;
    }
    return true;
}
int main() {
    scanf("%d%d",&n,&m);
    for (int i=1;i<=m;++i) {
        int u,v;
        scanf("%d%d",&u,&v);
        e[u].push_back(v),e[v].push_back(u);
    }
    if (!paint(1,1)) printf("%lld\n",(LL)n*(n-1)/2-m);
    else printf("%lld\n",(LL)(n/2)*((n+1)/2)-m);
    return 0;
}