#include <bits/stdc++.h>
using ll = long long;
#define int ll
using namespace std;
int N, K;
priority_queue<pair<int, int>> q;
signed main()
{
  cin >> N >> K;
  for (int i = 0; i < N; i++){
    int t, d;
    cin >> t >> d;
    q.push(make_pair(d, t));
  }
  vector<int> c(N + 1, 0);
  ll k = 0, res = 0;
  priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> mi;
  for (int i = 0; i < K; i++){
    auto x = q.top();
    q.pop();
    res += x.first;
    if (c[x.second] == 0){
      k++;
    }
    mi.push(x);
    c[x.second]++;
  }
  ll ma = res + k * k;
  for (int i = k + 1; i < K + 1; i++){
    while (c[mi.top().second] == 1) {
      mi.pop();
    }
    res -= mi.top().first;
    c[mi.top().second]--;
    mi.pop();
    while(!q.empty() && c[q.top().second]){
      q.pop();
    }
    if (q.empty()) {
      break;
    }
    res += q.top().first;
    c[q.top().second]++;
    q.top();
    ma = max(ma, res + i * i);
  }
  cout << ma << endl;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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 <bits/stdc++.h>
using ll = long long;
#define int ll
using namespace std;
int N, K;
priority_queue<pair<int, int>> q;
signed main()
{
  cin >> N >> K;
  for (int i = 0; i < N; i++){
    int t, d;
    cin >> t >> d;
    q.push(make_pair(d, t));
  }
  vector<int> c(N + 1, 0);
  ll k = 0, res = 0;
  priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> mi;
  for (int i = 0; i < K; i++){
    auto x = q.top();
    q.pop();
    res += x.first;
    if (c[x.second] == 0){
      k++;
    }
    mi.push(x);
    c[x.second]++;
  }
  ll ma = res + k * k;
  for (int i = k + 1; i < K + 1; i++){
    while (c[mi.top().second] == 1) {
      mi.pop();
    }
    res -= mi.top().first;
    c[mi.top().second]--;
    mi.pop();
    while(!q.empty() && c[q.top().second]){
      q.pop();
    }
    if (q.empty()) {
      break;
    }
    res += q.top().first;
    c[q.top().second]++;
    q.top();
    ma = max(ma, res + i * i);
  }
  cout << ma << endl;
}
```