Problem:
Score : 400 points

Problem Statement

There are N pieces of sushi. Each piece has two parameters: "kind of topping" t_i and "deliciousness" d_i.
You are choosing K among these N pieces to eat.
Your "satisfaction" here will be calculated as follows:

The satisfaction is the sum of the "base total deliciousness" and the "variety bonus".

The base total deliciousness is the sum of the deliciousness of the pieces you eat.

The variety bonus is x*x, where x is the number of different kinds of toppings of the pieces you eat.

You want to have as much satisfaction as possible.
Find this maximum satisfaction.

Constraints

1 \leq K \leq N \leq 10^5

1 \leq t_i \leq N

1 \leq d_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
t_1 d_1
t_2 d_2
.
.
.
t_N d_N

Output

Print the maximum satisfaction that you can obtain.

Sample Input 1

5 3
1 9
1 7
2 6
2 5
3 1

Sample Output 1

26

If you eat Sushi 1,2 and 3:

The base total deliciousness is 9+7+6=22.

The variety bonus is 2*2=4.

Thus, your satisfaction will be 26, which is optimal.

Sample Input 2

7 4
1 1
2 1
3 1
4 6
4 5
4 5
4 5

Sample Output 2

25

It is optimal to eat Sushi 1,2,3 and 4.

Sample Input 3

6 5
5 1000000000
2 990000000
3 980000000
6 970000000
6 960000000
4 950000000

Sample Output 3

4900000016

Note that the output may not fit into a 32-bit integer type.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include<queue>
#include<vector>
#include<set>
#include<map>
#include<algorithm>
#include<cstring>
#include<string>
#include<cassert>
#include<cmath>
#include<climits>
#include<iomanip>

using namespace std;

#define MOD 1000003
#define REP(i,n) for(ll (i)=0;(i)<(n);(i)++)
#define FOR(i,c) for(decltype((c).begin())i=(c).begin();i!=(c).end();++i)
#define ll long long
#define ull unsigned long long
#define all(hoge) (hoge).begin(),(hoge).end()
typedef pair<ll, ll> P;
const long long INF = 1LL << 60;
typedef vector<ll> Array;
typedef vector<Array> Matrix;


template<class T> inline bool chmin(T & a, T b) {
	if (a > b) {
		a = b;
		return true;
	}
	return false;
}
template<class T> inline bool chmax(T & a, T b) {
	if (a < b) {
		a = b;
		return true;
	}
	return false;
}


//グラフ関連
struct Edge {//グラフ
	ll to, cap, rev;
	Edge(ll _to, ll _cap, ll _rev) {
		to = _to; cap = _cap; rev = _rev;
	}
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
void add_edge(Graph& G, ll from, ll to, ll cap) {//最大フロー求める Ford-fulkerson
	G[from].push_back(Edge(to, cap, (ll)G[to].size()));
	G[to].push_back(Edge(from, cap, (ll)G[from].size() - 1));//最小カットの場合逆辺は0にする
}

ll max_flow_dfs(Graph & G, ll v, ll t, ll f, vector<bool> & used)
{
	if (v == t)
		return f;
	used[v] = true;
	for (int i = 0; i < G[v].size(); ++i) {
		Edge& e = G[v][i];
		if (!used[e.to] && e.cap > 0) {
			ll d = max_flow_dfs(G, e.to, t, min(f, e.cap), used);
			if (d > 0) {
				e.cap -= d;
				G[e.to][e.rev].cap += d;
				return d;
			}
		}
	}
	return 0;
}

ll max_flow(Graph & G, ll s, ll t)
{
	ll flow = 0;
	for (;;) {
		vector<bool> used(G.size());
		REP(i, used.size())used[i] = false;
		ll f = max_flow_dfs(G, s, t, INF, used);
		if (f == 0) {
			return flow;
		}
		flow += f;
	}
}

//最短経路(n>0だとだめ)
void Dijkstra(Graph& G, ll s, Array& d) {//O(|E|log|V|)
	d.resize(G.size());
	REP(i, d.size())d[i] = INF;
	d[s] = 0;
	priority_queue<P, vector<P>, greater<P>> q;
	q.push(make_pair(0, s));
	while (!q.empty()) {
		P a = q.top();
		q.pop();
		if (d[a.second] < a.first)continue;
		REP(i, G[a.second].size()) {
			Edge e = G[a.second][i];
			if (d[e.to] > d[a.second] + e.cap) {
				d[e.to] = d[a.second] + e.cap;
				q.push(make_pair(d[e.to], e.to));
			}
		}
	}
}

//最短経路(n<0でもok)
void WarshallFloyd(Graph& G, Matrix& d) {//O(V^3)
	d.resize(G.size());
	REP(i, d.size())d[i].resize(G.size());
	REP(i, d.size()) {
		REP(j, d[i].size()) {
			d[i][j] = INF;
		}
	}
	REP(i, G.size()) {
		REP(j, G[i].size()) {
			d[i][G[i][j].to] = G[i][j].cap;
		}
	}
	REP(i, G.size()) {
		REP(j, G.size()) {
			REP(k, G.size()) {
				chmin(d[j][k], d[j][i] + d[i][k]);
			}
		}
	}
}

class UnionFind {
	vector<int> data;
	int num;
public:
	UnionFind(int size) : data(size, -1), num(size) { }
	bool unionSet(int x, int y) {
		x = root(x); y = root(y);
		if (x != y) {
			if (data[y] < data[x]) swap(x, y);
			data[x] += data[y]; data[y] = x;
			num--;
		}
		return x != y;
	}
	bool findSet(int x, int y) {
		return root(x) == root(y);
	}
	int root(int x) {
		return data[x] < 0 ? x : data[x] = root(data[x]);
	}
	int size(int x) {
		return -data[root(x)];
	}
	int numSet() {
		return num;
	}
};

//nCr,nPr,modの逆元
class Combination {
public:
	Array fact;//n！
	Array inv;//n!の逆元
	ll mod;

	//modの逆元
	ll mod_inv(ll x) {
		ll n = mod - 2;
		ll res = 1LL;
		while (n > 0) {
			if (n & 1) res = res * x % mod;
			x = x * x % mod;
			n >>= 1;
		}
		return res;
	}
	ll nCr(ll n, ll r) {
		return ((fact[n] * inv[r] % mod) * inv[n - r]) % mod;
	}
	ll nPr(ll n, ll r) {
		return (fact[n] * inv[n - r]) % mod;
	}
	Combination(ll n, ll _mod) {
		mod = _mod;
		fact.resize(n + 1);
		fact[0] = 1;
		REP(i, n) {
			fact[i + 1] = (fact[i] * (i + 1LL)) % mod;
		}
		inv.resize(n + 1);
		REP(i, n + 1) {
			inv[i] = mod_inv(fact[i]);
		}
	}
};

//約数
void divisor(ll n, vector<ll>& ret) {
	for (ll i = 1; i * i <= n; i++) {
		if (n % i == 0) {
			ret.push_back(i);
			if (i * i != n) ret.push_back(n / i);
		}
	}
	sort(ret.begin(), ret.end());
}

//最大公約数
ll gcd(ll m, ll n) {
	if (n == 0)return m;
	return gcd(n, m % n);
}//gcd

//最小公倍数
ll lcm(ll m, ll n) {
	return m / gcd(m, n) * n;
}

//繰り返し自乗法
ll pow2(ll x, ll n) { //x^n 計算量O(logn)
	ll ans = 1ll;
	while (n > 0) {
		if ((n & 1) == 1) {
			ans = ans * x%MOD;
		}
		x = x * x%MOD; //一周する度にx, x^2, x^4, x^8となる
		n >>= 1; //桁をずらす n = n >> 1
	}
	return ans;
}

class MedSet {
public:
	multiset<ll> left, right;
	ll med;//中央値または中央値の左側
	MedSet() {}
	MedSet(ll _med) {

	}
	void insert(ll a) {
		if (left.size() == 0) {
			med = a;
			left.insert(med);
		}
		else {
			if (a < med) {
				left.insert(a);
				if (left.size() > right.size() + 1) {
					//left->right
					right.insert(*(--left.end()));
					left.erase(--left.end());
				}
				med = *(--left.end());
			}
			else {
				right.insert(a);
				if (right.size() > left.size()) {
					//right->left
					left.insert(*(right.begin()));
					right.erase(right.begin());
				}
				med = *(--left.end());
			}
		}
	}
};

//input
ll  N, M, L, K, A, B, C, D, Q;
string S;


int main()
{
	cin >> N >> K;
	vector<P> a(N,make_pair(0,0));
	REP(i, N) cin >> a[i].second >> a[i].first;
	
	sort(all(a), greater<P>());
	
	map<ll,ll> mp;
	ll y = 0;
	ll x = 0;
	REP(i, K) {
		y+=a[i].first;
		if (mp.find(a[i].second)==mp.end()) {
			mp[a[i].second] = 1;
			x++;
		}
		else {
			mp[a[i].second]++;
		}
	}
	ll ans = y+x*x;

	int j = K;
	for (int  i = K - 1; i > 0;i--) {
		if (mp[a[i].second] > 1) {
			while (j<N) {
				if (mp.find(a[j].second) == mp.end()) {
					mp[a[j].second] = 1;
					y += a[j].first - a[i].first;
					x++;
					chmax(ans,y + x * x);
					mp[a[i].second]--;
					j++;
					break;
				}
				else {
					j++;
				}		
			}
			if (j >= N) break;
		}
	}

	cout << ans << endl;

	return 0;
}