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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
using System.Numerics;

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            Solve();
            //Out.Flush();
            Read();
        }

        static void Solve()
        {
            var (N, K) = Slice2<long>();
            var td = new List<(long t, long d)>();
            for (var i = 0; i < N; ++i)
                td.Add(Slice2<long>());
            td.Sort((l, r) => r.d.CompareTo(l.d));//降順
            var used = new priority_queue<(long t, long d)>((l, r) => r.d.CompareTo(l.d));
            var kanri = new Dictionary<long, long>();//type,num
            var rems = new List<(long t, long d)>();
            var maxSum = 0L;
            //各種類の最大値を使用する
            foreach (var t in td)
            {
                if (used.num < K && !kanri.ContainsKey(t.t))
                {
                    kanri[t.t] = 1;
                    used.insert(t);
                    maxSum += t.d;
                }
                else
                    rems.Add(t);
            }
            rems.Reverse();//昇順
            //種類がK未満の場合、大きいのを使ってK個まで埋める
            while (used.num < K)
            {
                var le = rems.Last();
                rems.RemoveAt(rems.Count - 1);
                ++kanri[le.t];
                used.insert(le);
                maxSum += le.d;
            }
            //初期値
            var dp = maxSum + (long)kanri.Count * (long)kanri.Count;
            while (rems.Any())
            {
                //最小のものを1個捨てる
                var e = used.extract();
                //残りから最大のものを1個食べる
                var le = rems.Last();
                //交換しても意味ないので終了
                if (le.d <= e.d) break;
                used.insert(le);
                maxSum += le.d - e.d;
                ++kanri[le.t];
                --kanri[e.t];
                if (0 == kanri[e.t]) kanri.Remove(e.t);
                dp = Max(dp, maxSum + (long)kanri.Count * (long)kanri.Count);
                rems.RemoveAt(rems.Count - 1);
            }
            WriteLine(dp);
        }
        class priority_queue<T>
        {
            Comparison<T> cmp;
            T[] A = new T[2000000];
            // var pq = new priority_queue<long>((l, r) => l.CompareTo(r));
            // とすれば値の大きいものから優先
            public priority_queue(Comparison<T> c)
            {
                cmp = c;
            }
            public int num { get; private set; } = 0;
            public void insert(T v)
            {
                A[num] = v;
                ++num;
                increaseKey(num);
            }
            void increaseKey(int i)
            {
                while (1 < i && 0 < cmp(A[i - 1], A[i / 2 - 1]))
                {
                    var t = A[i - 1];
                    A[i - 1] = A[i / 2 - 1];
                    A[i / 2 - 1] = t;
                    i = i / 2;
                }
            }
            public T extract()
            {
                if (num < 1) return default(T);
                var max = A[0];
                A[0] = A[num - 1];
                --num;
                maxHeapify(1);
                return max;
            }
            void maxHeapify(int i)
            {
                var H = num;
                var l = left(i);
                var r = right(i);
                var largest = 0;
                if (l <= H && 0 < cmp(A[l - 1], A[i - 1])) { largest = l; } else { largest = i; }
                if (r <= H && 0 < cmp(A[r - 1], A[largest - 1])) { largest = r; }
                if (largest != i)
                {
                    var t = A[i - 1];
                    A[i - 1] = A[largest - 1];
                    A[largest - 1] = t;
                    maxHeapify(largest);
                }
            }
            int left(int l) => l * 2;
            int right(int r) => r * 2 + 1;
        }


        static long Mod = 998244353;
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static public (T1 a, T2 b) Slice<T1, T2>()
        {
            var t = ReadLine().Split();
            return (
            (T1)Convert.ChangeType(t[0], typeof(T1)),
            (T2)Convert.ChangeType(t[1], typeof(T2)));
        }
        static public (T a, T b) Slice2<T>()
        {
            var t = ReadLine().Split();
            return (
            (T)Convert.ChangeType(t[0], typeof(T)),
            (T)Convert.ChangeType(t[1], typeof(T)));
        }
        static public (T a, T b, T c) Slice3<T>()
        {
            var t = ReadLine().Split();
            return (
            (T)Convert.ChangeType(t[0], typeof(T)),
            (T)Convert.ChangeType(t[1], typeof(T)),
            (T)Convert.ChangeType(t[2], typeof(T)));
        }
        static public (T a, T b, T c, T d) Slice4<T>()
        {
            var t = ReadLine().Split();
            return (
            (T)Convert.ChangeType(t[0], typeof(T)),
            (T)Convert.ChangeType(t[1], typeof(T)),
            (T)Convert.ChangeType(t[2], typeof(T)),
            (T)Convert.ChangeType(t[3], typeof(T)));
        }
    }
}