#pragma GCC optimize ("O3")
#pragma GCC target ("avx")
#include "bits/stdc++.h" // define macro "/D__MAI"

using namespace std;
typedef long long int ll;

#define xprintf(fmt,...) fprintf(stderr,fmt,__VA_ARGS__)
#define debugv(v) {printf("L%d %s > ",__LINE__,#v);for(auto e:v){cout<<e<<" ";}cout<<endl;}
#define debuga(m,w) {printf("L%d %s > ",__LINE__,#m);for(int x=0;x<(w);x++){cout<<(m)[x]<<" ";}cout<<endl;}
#define debugaa(m,h,w) {printf("L%d %s >\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){cout<<(m)[y][x]<<" ";}cout<<endl;}}
#define ALL(v) (v).begin(),(v).end()
#define repeat(cnt,l) for(auto cnt=0ll;(cnt)<(l);++(cnt))
#define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt))
#define MD 1000000007ll
#define PI 3.1415926535897932384626433832795
#define EPS 1e-12
template<typename T1, typename T2> ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << "(" << p.first << ":" << p.second << ")"; return o; }
template<typename iterator> inline size_t argmin(iterator begin, iterator end) { return distance(begin, min_element(begin, end)); }
template<typename iterator> inline size_t argmax(iterator begin, iterator end) { return distance(begin, max_element(begin, end)); }
template<typename T> T& maxset(T& to, const T& val) { return to = max(to, val); }
template<typename T> T& minset(T& to, const T& val) { return to = min(to, val); }

mt19937_64 randdev(8901016);
inline ll rand_range(ll l, ll h) {
    return uniform_int_distribution<ll>(l, h)(randdev);
}

#ifdef __MAI
#define getchar_unlocked getchar
#define putchar_unlocked putchar
#endif
#ifdef __VSCC
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#endif
namespace {
#define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E)
    class MaiScanner {
    public:
        template<typename T> void input_integer(T& var) {
            var = 0;
            T sign = 1;
            int cc = getchar_unlocked();
            for (; cc<'0' || '9'<cc; cc = getchar_unlocked())
                if (cc == '-') sign = -1;
            for (; '0' <= cc&&cc <= '9'; cc = getchar_unlocked())
                var = (var << 3) + (var << 1) + cc - '0';
            var = var*sign;
        }
        inline int c() { return getchar_unlocked(); }
        inline MaiScanner& operator>>(int& var) {
            input_integer<int>(var);
            return *this;
        }
        inline MaiScanner& operator>>(long long& var) {
            input_integer<long long>(var);
            return *this;
        }
        inline MaiScanner& operator>>(string& var) {
            int cc = getchar_unlocked();
            for (; !isvisiblechar(cc); cc = getchar_unlocked());
            for (; isvisiblechar(cc); cc = getchar_unlocked())
                var.push_back(cc);
            return *this;
        }
        template<typename IT> void in(IT begin, IT end) {
            for (auto it = begin; it != end; ++it) *this >> *it;
        }
    };
}
MaiScanner scanner;



// 隣接頂点を保持する無向グラフ
class Graph {
public:
    size_t n;
    vector<vector<int>> vertex_to;

    Graph(size_t n) :n(n), vertex_to(n) {}

    void connect(int from, int to) {
        vertex_to[from].emplace_back(to);
        vertex_to[to].emplace_back(from);
    }
    void resize(size_t _n) {
        n = _n;
        vertex_to.resize(_n);
    }
};

ll m, n, kei;

Graph graph(1);


void answer_is_cliq() {
    ll fit = n*(n - 1) / 2;
    cout << (fit - m) << endl;
}

int main() {

    scanner >> n >> m;


    graph.resize(n);

    vector<pair<int, int>> edges;

    repeat(i, m) {
        int a, b;
        scanner >> a >> b;
        --a; --b;
        if (a > b) swap(a, b);
        graph.connect(a, b);
        edges.emplace_back(a, b);
    }

    vector<int> visited(n);
    // bool p7 = false;
    // 
    // function<void(int, int)> dfs = [&](int idx, int from) {
    //     
    //     int dist = visited[idx];
    //     p7 |= dist - 1 >= 7;
    // 
    //     for (int to : graph.vertex_to[idx]) {
    //         if (to != from && !visited[idx]) {
    //             visited[idx] = dist;
    //             dfs(to, idx);
    //         }
    //     }
    // };
    // visited[0] = 1;
    // dfs(0, -1);
    // 
    // int far = distance(visited.begin(),max_element(ALL(visited)));
    // fill(ALL(visited), 0);
    // visited[far] = 1;
    // dfs(far, -1);
    // 
    // if (p7) {
    //     answer_is_cliq();
    //     return 0;
    // }

    // sample1
    // 距離が奇数の頂点と辺が張れる => FAIL
    // P7, 完全グラフに遷移する
    // K3を含む　完全グラフに遷移にできる

    // 例外ケースのみを洗い出せばおｋ？
    // 頂点数6以下の二部グラフ

    // 二部グラフかどうか判定する

    sort(ALL(edges));
    set<int> setA, setB;


    fill(ALL(visited), 0);
    function<void(int, int)> dfs2 = [&](int idx, int from) {
        visited[idx] = 1;

        for (int to : graph.vertex_to[idx]) {
            int u = idx;
            int v = to;

            if (setA.count(u)) {
                if (setA.count(v)) {
                    answer_is_cliq(); exit(0);
                }
                setB.insert(v);
            }
            else if (setB.count(u)) {
                if (setB.count(v)) {
                    answer_is_cliq(); exit(0);
                }
                setA.insert(v);
            }
            else if (setA.count(v)) {
                if (setA.count(u)) {
                    answer_is_cliq(); exit(0);
                }
                setB.insert(u);
            }
            else if (setB.count(v)) {
                if (setB.count(u)) {
                    answer_is_cliq(); exit(0);
                }
                setA.insert(u);
            }
            else {
                setA.insert(u);
                setB.insert(v);
            }
        }

        for (int to : graph.vertex_to[idx]) {

            if (to != from && !visited[to]) {
                
                dfs2(to, idx);
            }
        }
    };
    dfs2(0, -1);


    // for (auto edge : edges) {
    //     int u = edge.first;
    //     int v = edge.second;
    // 
    //     if (setA.count(u)) {
    //         if (setA.count(v)) {
    //             answer_is_cliq(); return 0;
    //         }
    //         setB.insert(v);
    //     }
    //     else if (setB.count(u)) {
    //         if (setB.count(v)) {
    //             answer_is_cliq(); return 0;
    //         }
    //         setA.insert(v);
    //     }
    //     else if (setA.count(v)) {
    //         if (setA.count(u)) {
    //             answer_is_cliq(); return 0;
    //         }
    //         setB.insert(u);
    //     }
    //     else if (setB.count(v)) {
    //         if (setB.count(u)) {
    //             answer_is_cliq(); return 0;
    //         }
    //         setA.insert(u);
    //     }
    //     else {
    //         setA.insert(u);
    //         setB.insert(v);
    //     }
    // }

    ll fit = setA.size()*setB.size();
    cout << (fit - m) << endl;

    return 0;
}

Measured memory_bytes: 12148