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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Diagnostics;

namespace PaizaSkillCheck
{
    public class Program
    {
        public static void Main(string[] args)
        {
            int[] usingKind = new int[100001];
            int kind_count = 0;

            ulong nowPoint = 0;
            ulong maxPoint = 0;

            string[] line = Console.ReadLine().Split(' ');
            int n = int.Parse(line[0]);
            int k = int.Parse(line[1]);

            //  すべての寿司を取得
            List<Sushi> sushiList = new List<Sushi>(n);
            for (int i = 0; i < n; i++)
            {
                line = Console.ReadLine().Split(' ');
                sushiList.Add(new Sushi(int.Parse(line[0]), int.Parse(line[1])));
            }
            //  寿司を降順ソート
            sushiList.Sort((a, b) => b.point - a.point);


            //  上からK個寿司を取る
            List<Sushi> list = sushiList.Take(k).ToList();

            //  寿司の種類ごとに数を数える
            //  現在のポイントを数える
            foreach (Sushi sushi in list)
            {
                if (usingKind[sushi.kind] == 0)
                {
                    kind_count++;
                }
                usingKind[sushi.kind]++;
                nowPoint += (ulong) sushi.point;
            }
            //  現在の選択中の寿司を昇順ソート
            list.Sort((a, b) => b.CompareTo(a));

            //  最低限必要なループ回数
            int needLoopCount = k - kind_count;

            //  現在のポイント
            maxPoint = nowPoint + (ulong)(kind_count * kind_count);

            //  現在選択中の種類が選択できる数以下なら
            while(kind_count < k)
            {
                //  一番小さく　かつ　種類が重複している寿司を削除
                Sushi target = null;
                foreach (Sushi sushi in list)
                {
                    if (usingKind[sushi.kind] > 1)
                    {
                        usingKind[sushi.kind]--;
                        target = sushi;
                        nowPoint -= (ulong) sushi.point;

                        break;
                    }
                }

                //  重複している寿司がなければ終了
                if (target == null)
                {
                    Console.WriteLine(maxPoint);
                    Console.ReadLine();
                    return;
                }
                list.Remove(target);

                //  一番大きく　かつ　種類が重複しない寿司を追加
                foreach(Sushi sushi in sushiList)
                {
                    if (usingKind[sushi.kind] == 0)
                    {
                        usingKind[sushi.kind]++;
                        kind_count++;
                        nowPoint += (ulong) sushi.point;
                        break;
                    }
                }

                //  ポイントを計算
                maxPoint = Math.Max(maxPoint, nowPoint + (ulong) (kind_count * kind_count));
            }

            Console.WriteLine(maxPoint);
            Console.ReadLine();
        }

        /// <summary>
        /// 寿司オブジェクト
        /// </summary>
        public class Sushi : IComparable
        {
            public int kind;
            public int point;

            public Sushi(int t, int d)
            {
                this.kind = t;
                this.point = d;
            }

            public override string ToString()
            {
                return string.Format("{0}, {1}", kind, point);
            }

            public int CompareTo(Object obj)
            {
                Sushi sushi = (Sushi) obj;

                return (sushi?.point ?? 0) - this.point;
            }
        }
    }
}