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;

class Program
{
    static void Main(string[] args)
    {
        var N = sc.ReadInt();
        var K = sc.ReadInt();
        var TDs = new TD[N];
        for (int i = 0; i < N; i++)
        {
            TDs[i] = new TD(sc.ReadInt(), sc.ReadInt());
        }

        long sum = 0;
        var typeCounts = new int[N + 1];
        TDs = TDs.OrderByDescending(x => x.D).ToArray();
        var types = 0;
        var s = new Stack<TD>();
        var q = new Queue<TD>();
        for (int i = 0; i < N; i++)
        {
            if (i < K)
            {
                sum += TDs[i].D;
                typeCounts[TDs[i].T]++;
                if (typeCounts[TDs[i].T] == 1) types++;
                s.Push(TDs[i]);
            }
            else
            {
                q.Enqueue(TDs[i]);
            }
        }
        var ans = sum + types * types;

        long next = 0;
        long nextSum = sum;
        while (q.Count > 0 && s.Count > 0)
        {
            // 種類が増える候補を取り出す
            var x = q.Dequeue();
            if (typeCounts[x.T] == 0)
            {
                typeCounts[x.T]++;
                types++;

                // 種類が減らない候補を取り出す
                if (s.Count > 0)
                {
                    var flag = false;
                    TD y = s.Peek();
                    while (s.Count > 0)
                    {
                        y = s.Pop();
                        if (typeCounts[y.T] > 1)
                        {
                            typeCounts[y.T]--;
                            flag = true;
                            break;
                        }
                    }
                    if (flag == false) break;
                    // 入れ替えたときに答えが増える場合は交換する
                    nextSum = nextSum - y.D + x.D;
                    next = nextSum + types * types;
                    if (ans < next)
                    {
                        ans = next;
                    }
                }
            }
        }

        Console.WriteLine(ans);
    }


    struct TD
    {
        public int T { get; set; }
        public int D { get; set; }
        public TD(int _T, int _D)
        {
            this.T = _T;
            this.D = _D;
        }
    }

    static int MOD = (int)1e9 + 7;
    static int INF = (int)1e7 + 1;
    static long LINF = (long)1e13 + 1;
    static Scanner sc = new Scanner();
}

class Scanner
{
    string[] S = new string[0];
    int Index = 0;
    char[] Separators = new char[] { ' ' };

    public string Next()
    {
        if (this.Index < this.S.Length) return this.S[this.Index++];
        var line = "";
        while (line == "") line = Console.ReadLine();
        this.S = line.Split(this.Separators, StringSplitOptions.RemoveEmptyEntries);
        if (this.S.Length == 0) return this.Next();
        this.Index = 0;
        return this.S[this.Index++];
    }
    public string ReadStr()
    {
        return this.Next();
    }
    public char ReadChar()
    {
        return this.Next()[0];
    }
    public int ReadInt()
    {
        return int.Parse(this.Next());
    }
    public uint ReadUInt()
    {
        return uint.Parse(this.Next());
    }
    public long ReadLong()
    {
        return long.Parse(this.Next());
    }
    public double ReadDouble()
    {
        return double.Parse(this.Next());
    }
    public int[] ReadIntArray(int n)
    {
        var array = new int[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadInt();
        }
        return array;
    }
    public long[] ReadLongArray(int n)
    {
        var array = new long[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadLong();
        }
        return array;
    }
    public double[] ReadDoubleArray(int n)
    {
        var array = new double[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadDouble();
        }
        return array;
    }
    public char[] ReadCharArray(int n)
    {
        var array = new char[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadChar();
        }
        return array;
    }
    public string[] ReadStrArray(int n)
    {
        var array = new string[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadStr();
        }
        return array;
    }
}

class Debug
{
    public static void Dump<T>(T[,] array)
    {
#if !DEBUG
        return;
#endif
        Console.WriteLine();
        var h = array.GetLength(0);
        var w = array.GetLength(1);

        for (int r = 0; r < h; r++)
        {
            for (int c = 0; c < w; c++)
            {
                Console.Write(array[r, c]);
                Console.Write(" ");
            }
            Console.WriteLine();
        }
        Console.WriteLine();
    }
    public static void Dump<T>(T[] array)
    {
#if !DEBUG
        return;
#endif
        Console.WriteLine();
        Console.WriteLine(string.Join(" ", array));
        Console.WriteLine();
    }
}