#include <iostream>
#include <algorithm>
#include <vector>
#include <utility>
#include <map>
#define rep(i,n) for(int i=0;i<n;++i)
#define rep1(i,n) for(int i=1;i<=n;++i)
using namespace std;
typedef long long ll;
bool comp(pair<ll,int> &a,pair<ll,int> &b){
  return a.first>b.first;
}
int main()
{
  int n,k;cin >> n >> k;
  vector<pair<ll,int>> p(n);
  rep(i,n){
    int t;ll d;
    cin >> t >> d;
    p[i] = {d,t};
  }

  sort(p.begin(), p.end(),comp);
  ll sum = 0;
  ll num = 0;
  map<ll,int> mp;
  vector<ll> a;
  rep(i,k){
    if(mp[p[i].second]==0) num++;
    else a.push_back(p[i].first);
    sum += p[i].first;
    mp[p[i].second]++;
  }
  vector<ll> b;
  for(int i=k;i<n;++i){
    if(mp[p[i].second]==0) b.push_back(p[i].first);
    mp[p[i].second]++;
  }

  reverse(a.begin(), a.end());
  ll res = num*num+sum;
  rep(i,min(a.size(),b.size())){
    sum -= a[i]-b[i];
    num++;
    res = max(res,num*num+sum);
  }
  cout << res << "\n";
  return 0;
}

### Prompt

Your task is to create a cpp solution to the following problem:

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.

Examples

Input

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


Output

26


Input

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


Output

25


Input

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


Output

4900000016

### Response

```cpp
#include <iostream>
#include <algorithm>
#include <vector>
#include <utility>
#include <map>
#define rep(i,n) for(int i=0;i<n;++i)
#define rep1(i,n) for(int i=1;i<=n;++i)
using namespace std;
typedef long long ll;
bool comp(pair<ll,int> &a,pair<ll,int> &b){
  return a.first>b.first;
}
int main()
{
  int n,k;cin >> n >> k;
  vector<pair<ll,int>> p(n);
  rep(i,n){
    int t;ll d;
    cin >> t >> d;
    p[i] = {d,t};
  }

  sort(p.begin(), p.end(),comp);
  ll sum = 0;
  ll num = 0;
  map<ll,int> mp;
  vector<ll> a;
  rep(i,k){
    if(mp[p[i].second]==0) num++;
    else a.push_back(p[i].first);
    sum += p[i].first;
    mp[p[i].second]++;
  }
  vector<ll> b;
  for(int i=k;i<n;++i){
    if(mp[p[i].second]==0) b.push_back(p[i].first);
    mp[p[i].second]++;
  }

  reverse(a.begin(), a.end());
  ll res = num*num+sum;
  rep(i,min(a.size(),b.size())){
    sum -= a[i]-b[i];
    num++;
    res = max(res,num*num+sum);
  }
  cout << res << "\n";
  return 0;
}

```