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 <iomanip>
#include <string>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <stack>
#include <queue>
#include <bitset>
#include <numeric>
#include <cassert>
#ifdef DEBUG
#include "./Lib/debug.hpp"
#else
#define dump(...)
template<class T>inline auto d_val(T a, T b) { return a; }
#endif

/* (=＾o＾=) */
#define int ll

/* macro */
#define FOR(i, b, e) for(ll i = (ll)(b); i < (ll)(e); ++i)
#define RFOR(i, b, e) for(ll i = (ll)(e-1); i >= (ll)(b); --i)
#define REP(i, n) FOR(i, 0, n)
#define RREP(i, n) RFOR(i, 0, n)
#define REPC(x,c) for(const auto& x:(c))
#define REPI2(it,b,e) for(auto it = (b); it != (e); ++it)
#define REPI(it,c) REPI2(it, (c).begin(), (c).end())
#define RREPI(it,c) REPI2(it, (c).rbegin(), (c).rend())
#define REPI_ERACE2(it, b, e) for(auto it = (b); it != (e);)
#define REPI_ERACE(it, c) REPI_ERACE2(it, (c).begin(), (c).end())
#define ALL(x) (x).begin(),(x).end()
#define cauto const auto&
/* macro func */
#define SORT(x) do{sort(ALL(x));}while(false)
#define RSORT(x) do{sort((x).rbegin(),(x).rend());}while(false)
#define UNIQUE(v) do{v.erase( unique(v.begin(), v.end()), v.end() );}while(false)
#define MAX(x,y) do{x = std::max(x,y);}while(false)
#define MIN(x,y) do{x = std::min(x,y);}while(false)
#define BR do{cout<<"\n";}while(false)

/* type define */
using ll = long long;
using PAIR = std::pair<ll, ll>;
using VS = std::vector<std::string>;
using VL = std::vector<long long>;
using VVL = std::vector<VL>;
using VVVL = std::vector<VVL>;
using VD = std::vector<double>;
template<class T>
using V = std::vector<T>;

/* using std */
using std::cout;
constexpr char endl = '\n';
using std::cin;
using std::sort;
using std::pair;
using std::string;
using std::stack;
using std::queue;
using std::vector;
using std::list;
using std::map;
using std::unordered_map;
using std::multimap;
using std::unordered_multimap;
using std::set;
using std::unordered_set;
using std::unordered_multiset;
using std::multiset;
using std::bitset;
using std::priority_queue;

/* constant value */
constexpr ll MOD = 1000000007;
//constexpr ll MOD = 998244353;

/* Initial processing  */
struct Preprocessing { Preprocessing() { std::cin.tie(0); std::ios::sync_with_stdio(0); }; }_Preprocessing;

/* Remove the source of the bug */
signed pow(signed, signed) { assert(false); return -1; }

/* define hash */
namespace std { template <>	class hash<std::pair<ll, ll>> { public:	size_t operator()(const std::pair<ll, ll>& x) const { return hash<ll>()(1000000000 * x.first + x.second); } }; }

/* input */
template<class T> std::istream& operator >> (std::istream& is, vector<T>& vec) { for (T& x : vec) is >> x; return is; }

//=============================================================================================

signed main() {
	ll n, m;
	cin >> n >> m;
	unordered_multimap<ll, ll> graph;
	REP(i, m) {
		ll a, b;
		cin >> a >> b;
		--a; --b;
		graph.emplace(a, b);
	}

	ll max = 0;

	VL flg(n); flg[0] = 1;
	queue<ll> q; q.emplace(0);
	while (!q.empty()) {
		ll from = q.front();
		q.pop();

		auto range = graph.equal_range(from);
		REPI2(itr, range.first, range.second) {
			ll to = itr->second;
			if (flg[to] == 0) {
				q.emplace(to);
				flg[to] = flg[from] * -1;
				continue;
			}
			if (flg[to] == flg[from]) {
				max = n * (n - 1) / 2;
			}
		}
	}

	if (max > 0) {
		cout << max - m << endl;
		return 0;
	}

	ll a = 0, b = 0;
	REPC(x, flg) { ++((x == 1) ? a : b); }
	max = a * b;
	dump(a, b, flg);
	cout << max - m << endl;
}