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 <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <stack>
#include <queue>
#include <functional>
#include <algorithm>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <vector>
#include <array>
#include <tuple>
#include <utility>
#include <numeric>
#include <iomanip>
#include <cctype>
#include <cmath>
#include <assert.h>
#include <cstdlib>
#include <list>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using PII = pair<int, int>;
using PLL = pair<ll, ll>;

template<typename T1, typename T2> ostream& operator<<(ostream& s, const pair<T1, T2>& p) {
    return s << "(" << p.first << ", " << p.second << ")";
}
template<typename T> ostream& operator<<(ostream& s, const vector<T>& v) {
    s << "[";
    for (int i = 0; i < v.size(); i++) s << (i == 0 ? "" : ", ") << v[i];
    s << "]";
    return s;
}

#define ALL(a) (a).begin(), (a).end()

vector<int> graph[200005];
int color[200005];

bool dfs(int v, int d) {
    color[v] = d;

    bool res = false;
    for (int to : graph[v]) {
        if (color[to] < 0) {
            res = res || dfs(to, d ^ 1);
        } else if (color[to] != (d ^ 1)) {
            return true;
        }
    }
    return res;
}

int main() {
    ll N, M;
    cin >> N >> M;

    for (int i = 0; i < M; i++) {
        int A, B;
        cin >> A >> B;
        A--; B--;
        graph[A].push_back(B);
        graph[B].push_back(A);
    }

    memset(color, -1, sizeof(color));

    bool flag = dfs(0, 0);
    if (flag) {
        cout << (N * (N - 1)) / 2 - M << endl;
    } else {
        ll cnt = 0;
        for (int i = 1; i < N; i += 2) {
            cnt += N - i;
        }
        cout << cnt - M << endl;
    }

    return 0;
}