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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> P;
typedef pair<int,int> Pi;
#define rep(i,n) for(ll i=0;i<n;i++)
#define FOR(i,a,b) for(ll i=a;i<b;i++)
#define fi first
#define se second
#define endl "\n"

template<typename T> inline bool chmax(T &a, T b){if(a<b){a=b;return true;}return false;}
template<typename T> inline bool chmin(T &a, T b){if(a>b){a=b;return true;}return false;}
template<typename T> ostream& operator<<(ostream& s,const complex<T>& d) {return s<<"("<<d.real()<<", "<<d.imag()<< ")";}
template<typename T1, typename T2> ostream& operator<<(ostream& s,const pair<T1,T2>& d) {return s<<"("<<d.first<<", "<<d.second<<")";}
template<typename T> ostream& operator<<(ostream& s, const vector<T>& d){int len=d.size();rep(i,len){s<<d[i];if(i<len-1) s<<" ";}return s;}
template<typename T> ostream& operator<<(ostream& s,const vector<vector<T>>& d){int len=d.size();rep(i,len){s<<d[i]<<endl;}return s;}
template<typename T> ostream& operator<<(ostream& s,const set<T>& v){s<<"{ ";for(auto itr=v.begin();itr!=v.end();++itr) {if (itr!=v.begin()) {s<< ", ";}s<<(*itr);}s<<" }";return s;}
template<typename T> ostream& operator<<(ostream& s,const multiset<T>& v){s<<"{ ";for(auto itr=v.begin();itr!=v.end();++itr) {if (itr!=v.begin()) {s<< ", ";}s<<(*itr);}s<<" }";return s;}
template<typename T1, typename T2> ostream& operator<<(ostream& s,const map<T1,T2>& m){s<<"{"<<endl;for(auto itr=m.begin();itr!=m.end();++itr){s<<" "<<(*itr).first<<" : "<<(*itr).second<<endl;}s<<"}"<<endl;return s;}

const ll mod=1e9+7;
const ll inf=1e17;
const int INF=1e9;
const double EPS=1e-10;
const double PI=acos(-1);

int main(){
	cin.tie(0);ios::sync_with_stdio(false);
	ll n,k;
	cin>>n>>k;
	vector<P> g(n);
	rep(i,n){
		cin>>g[i].fi>>g[i].se;
	}
	sort(begin(g),end(g),[](const P &a,const P &b){
		return a.se>b.se;
	});
	ll ans=0;
	map<ll,ll> mp;
	rep(i,k){
		ans+=g[i].se;
		mp[g[i].fi]++;
	}
	priority_queue<P,vector<P>,greater<P>> que;//(美味しさ,ネタ)
	rep(i,k){
		if(mp[g[i].fi]>=2){
			que.push({g[i].se,g[i].fi});
		}
	}
	ans+=(ll)mp.size()*(ll)mp.size();
	ll now=ans;
	FOR(i,k,n){//美味しさを引き換えに種類数を増やしていく
		if(mp.count(g[i].fi)) continue;//既に含まれていたら選ぶ意味なし
		while(!que.empty()){
			auto hoge=que.top();
			que.pop();
			if(mp[hoge.se]==1) continue;
			now-=hoge.fi;
			now+=g[i].se;
			mp[hoge.se]--;
			mp[g[i].fi]++;
			break;
		}
		now+=(ll)mp.size()*(ll)mp.size()-((ll)mp.size()-1)*((ll)mp.size()-1);
		chmax(ans,now);
	}
	cout<<ans<<endl;
}