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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
using Pair = System.Tuple<int, int>;
using Edge = System.Tuple<int, int, long>;
//using Debug;
//using static System.Globalization.CultureInfo;

class Program
{
    static void Main(string[] args)
    {
        Solve();
        //WriteLine(Solve());
    }
    class G:IComparable<G>
    {
        public int t;
        public int d;
        public G(int[] td)
        {
            t = td[0];
            d = td[1];
        }
        public int CompareTo(G g)
            => d.CompareTo(g.d);
    }
    static void Solve()
    {
        var nk = Input.ar;
        var gs = Enumerable.Repeat(0, nk[0]).Select(_ => new G(Input.ar)).ToArray();
        gs = gs.OrderByDescending(v => v).ToArray();
        var pq = new PriorityQueue<G>(new G(new[] { -1, int.MaxValue }), false);
        var ct = 0L;
        var ts = new bool[nk[0]];
        var sum = 0L;
        var res = 0L;
        for(var i = 0; i < nk[0]; i++)
        {
            if (i < nk[1])
            {
                sum += gs[i].d;
                if (!ts[gs[i].t - 1])
                {
                    ct++;
                    ts[gs[i].t - 1] = true;
                }
                else
                    pq.Enqueue(gs[i]);
            }
            else
            {
                if (ts[gs[i].t - 1]||pq.isEmpty) continue;
                ct++;
                sum += gs[i].d;
                ts[gs[i].t - 1] = true;
                sum -= pq.Dequeue().d;
            }
            res = Max(res, ct * ct + sum);
        }
        WriteLine(res);
    }
}

public class Input
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public static char[][] gred(int h) 
        => Enumerable.Repeat(0, h).Select(v => read.ToCharArray()).ToArray();
    public static int[][] ar2D(int num)
        => Enumerable.Repeat(0, num).Select(v => ar).ToArray();
    public static long[][] arL2D(int num)
        => Enumerable.Repeat(0, num).Select(v => arL).ToArray();
    public const long Inf = (long)1e18;
    public const double eps = 1e-6;
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}

public class PriorityQueue<T> where T : IComparable<T>
{
    private readonly List<T> items;
    private T MinValue { get; }//一番優先度が低い値

    public bool IsMax { get; }
    public int Size { get { return items.Count; } }
    public bool isEmpty { get { return items.Count == 0; } }
    
    public PriorityQueue(T MinValue,bool IsMax=true)
    {
        this.items = new List<T>();
        this.IsMax = IsMax;
        this.MinValue = MinValue;
    }

    private int Parent(int num)
    {
        return (int)Math.Ceiling((double)num / 2) - 1;
    }
    private int Left(int num)
    { 
        return 2 * num + 1;
    }
    private int Right(int num)
    { 
        return 2 * (num + 1);
    }

    private void MaxHeapify(int num)
    {
        var left = Left(num);
        var right = Right(num);
        var largest = 0;
        if (Size >= left + 1 && items[left].CompareTo(items[num]) == 1)
            largest = left;
        else largest = num;
        if (Size >= right + 1 && items[right].CompareTo(items[largest]) == 1)
            largest = right;
        if (largest != num)
        {
            var value = items[largest];
            items[largest] = items[num];
            items[num] = value;
            MaxHeapify(largest);
        }
    }

    private void MinHeapify(int num)
    {
        var left = Left(num);
        var right = Right(num);
        var smallest = 0;
        if (Size >= left + 1 && items[num].CompareTo(items[left]) == 1) smallest = left;
        else smallest = num;
        if (Size >= right + 1 && items[smallest].CompareTo(items[right]) == 1) smallest = right;
        if (smallest != num)
        {
            var value = items[smallest];
            items[smallest] = items[num];
            items[num] = value;
            MinHeapify(smallest);
        }
    }

    private void BuildHeap()
    {
        for (var i = (int)Math.Ceiling((double)Size / 2) - 1; i >= 0; i--)
        {
            if (IsMax) MaxHeapify(i);
            else MinHeapify(i);
        }
    }
    

    private bool ChangeKey(int index, T reValue)
    {
        if (IsMax && items[index].CompareTo(reValue) == 1)
            return false;
        if (!IsMax && items[index].CompareTo(reValue) == -1)
            return false;
        items[index] = reValue;
        if (IsMax)
        {
            while (index > 0 && items[Parent(index)].CompareTo(items[index]) == -1)
            {
                var value = items[Parent(index)];
                items[Parent(index)] = items[index];
                items[index] = value;
                index = Parent(index);
            }
        }
        else
        {
            while (index > 0 && items[Parent(index)].CompareTo(items[index]) == 1)
            {
                var value = items[Parent(index)];
                items[Parent(index)] = items[index];
                items[index] = value;
                index = Parent(index);
            }
        }
        return true;
    }

    public T Peek { get { return items[0]; } }

    public T Dequeue()
    {
        if (Size <= 0) return default(T);
        var value = items[0];
        items[0] = items[Size - 1];
        items.RemoveAt(Size - 1);
        if (IsMax) MaxHeapify(0);
        else MinHeapify(0);
        return value;
    }

    public bool Enqueue(T key)
    {
        items.Add(MinValue);
        return ChangeKey(Size-1, key);
    }

    private bool Delete(int index)
    {
        if (index >= Size)
            return false;
        var value = items[index];
        items[index] = items[Size - 1];
        items[Size - 1] = value;
        items.RemoveAt(Size - 1);
        if (IsMax) MaxHeapify(0);
        else MinHeapify(0);
        return true;
    }
}