#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template<typename T> bool mmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template<typename T> bool mmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template<typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template<typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;
#define FI first
#define SE second
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((lint)(x).size())
#define POW2(n) (1LL << (n))

struct UndirectedGraph
{
    using pint = pair<int, int>;

    int V, E;

    vector<vector<pint>> to; // to[v1] = [pair(v2, edgeId)]
    vector<pint> edges; // edges[edgeId] = (v1, v2)

    UndirectedGraph(): V(0), E(0) {}
    UndirectedGraph(int V): V(V), E(0)
    {
        to.resize(V);
    }

    void add_edge(int v1, int v2)
    {
        to[v1].push_back(pint(v2, E));
        to[v2].push_back(pint(v1, E));
        edges.push_back(pint(v1, v2));
        E++;
    }

    // v0の連結成分からなる部分グラフが2部グラフかどうか判定
    // 最悪O(N^2)を避けるためbip_color, bip_visitedを一々初期化
    // していない，このため動的にグラフを更新する場合に非対応
    vector<int> bip_color; // 2部グラフ判定彩色 1, 2で塗る
    vector<bool> bip_visited;
    bool is_subgraph_bipartite(int v0)
    {
        bip_color.resize(V);
        bip_visited.resize(V);
        if (!bip_color[v0]) bip_color[v0] = 1;
        queue<int> vs_pending;
        vs_pending.push(v0);
        while (!vs_pending.empty())
        {
            int now = vs_pending.front();
            vs_pending.pop();
            if (bip_visited[now]) continue;

            bip_visited[now] = true;
            for (auto nxt : to[now])
            {
                if (bip_color[nxt.first] == bip_color[now]) return false;
                else if (bip_color[nxt.first] == 0)
                {
                    bip_color[nxt.first] = 3 - bip_color[now];
                    vs_pending.push(nxt.first);
                }
            }
        }

        return true;
    }
};

vector<vector<int>> e;
vector<int> c;

void dfs(int now, int x) {
    c[now] = x;
    for (auto nxt : e[now]) if (c[nxt] == -1) {
        dfs(nxt, 1 - x);
    }
}
int main()
{
    lint N, M;
    cin >> N >> M;
    e.resize(N);
    c.assign(N, -1);
    UndirectedGraph graph(N);
    REP(_, M) {
        int a, b;
        cin >> a >> b;
        graph.add_edge(a - 1, b - 1);
        e[a - 1].push_back(b - 1);
        e[b - 1].push_back(a - 1);
    }
    if (graph.is_subgraph_bipartite(0)) {
        dfs(0, 1);
        lint o = accumulate(ALL(c), 0LL);
        cout << o * (N - o) - M << endl;
    }
    else {
        cout << N * (N - 1) / 2 - M << endl;
    }
}


Measured memory_bytes: 13684