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# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

namespace CSharpSample01
{

    class Sushi
    {
        internal int neta;
        internal int umasa;

        public Sushi(int n, int u)
        {
            this.neta = n;
            this.umasa = u;
        }
    }


    class Program
    {

        static void Main(string[] args)
        {
            string[] str = Console.ReadLine().Split(' ');
            int N = int.Parse(str[0]);
            int K = int.Parse(str[1]);

            var dic = new Dictionary<long, long>();
            var data = new List<Sushi>();

            //入力
            for (int i = 0; i < N; i++)
            {
                string[] sushi = Console.ReadLine().Split(' ');
                int neta = int.Parse(sushi[0]);
                int umasa = int.Parse(sushi[1]);
                Sushi s = new Sushi(neta, umasa);
                data.Add(s);
            }

            data.Sort((a, b) => b.umasa - a.umasa);

            var sdata = new List<Sushi>();
            var ssdata = new List<Sushi>();
            int u = 0;
            var dic_type = new Dictionary<int, int>();
            int type = 0;

            //初期集合SとSSを作る
            foreach (var s in data)
            {
                if (u < K)
                {
                    //Console.WriteLine($"neta = {s.neta} umasa = {s.umasa}");
                    sdata.Add(s);
                    if (!dic_type.ContainsKey(s.neta))
                    {
                        dic_type[s.neta] = s.umasa;  //S内に入っているネタの種類を記録
                        type++;
                    }
                }
                else
                {
                    if(!dic_type.ContainsKey(s.neta)) ssdata.Add(s);
                }
                u++;
            }

            //初期集合SとSSの作成完了

            //x種類のネタを選ぶときの基礎おいしさの最大f[x]を求める
            //xは現在のtypeからKまで(K個しか選べないので最大K種類しか選べない)

            long[] f = new long[K + 1];
            f[type] = sdata.Sum(x => (long)x.umasa);

            bool flag = false;
            int starttype = type;
            while (true)
            {
                //Sから見つける
                for (int i = sdata.Count - 1; i > 0; i--)
                {
                    if (sdata[i].neta == sdata[i - 1].neta)
                    {
                        Sushi tmp = sdata[i];
                        sdata.Remove(sdata[i]);  //Sから抜かす
                        f[type + 1] = f[type] - tmp.umasa;
                        break;
                    }

                    if (i == 1) flag = true;
                }

                if (flag) break;

                //SSから見つける
                for (int i = 0; i < ssdata.Count; i++)
                {
                    //今S内にないネタで最大をsSS内から見つける
                    if (!dic_type.ContainsKey(ssdata[i].neta))
                    {
                        Sushi tmp = ssdata[i];
                        ssdata.RemoveAll(s => s.neta == tmp.neta);  //SSから抜かす
                        sdata.Add(tmp);  //Sに入れる
                        f[type + 1] += tmp.umasa;  //新しいfを更新               
                        type++;   //S内の種類数を増やす   
                        break;
                    }

                    if (i == ssdata.Count - 1) flag = true;
                }

                if (flag) break;
                if (type == K) break;

            }

            //今まで求めたfから(starttype から typeまで)gを求めて
            //最大のgを見つける(long gの更新制)
            long g = 0;
            for (long i = starttype; i <= type; i++)
            {
                if (g < f[i] + i * i) g = f[i] + i * i;
            }

            Console.WriteLine(g);

        }
    }
}