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 Input;

public class Prog
{
    private const int INF = 1000000007;
    public static void Main()
    {
        int N = NextInt();
        int K = NextInt();
        PriorityQueue<int, int[]> PQ = new PriorityQueue<int, int[]>(false);
        for (int i = 0; i < N; i++)
        {
            int[] td = LineInt();
            //int[] td = new int[2] { i, 1_000_000_000 };
            PQ.Add(td[1], td);
        }
        HashSet<int> color = new HashSet<int>();
        PriorityQueue<int, int> DelQ = new PriorityQueue<int, int>();
        long ans = 0;
        for (int i = 0; i < K; i++)
        {
            int[] A = PQ.Take();
            if (color.Contains(A[0])) DelQ.Add(A[1], A[1]);
            else color.Add(A[0]);
            ans += A[1];
        }
        long max = ans + (long)color.Count() * color.Count();
        for (int i = 0; i < (N - K); i++)
        {
            //Swaping code
            if (DelQ.Count() == 0 || PQ.Count() == 0) break;
            int[] A = PQ.Take();
            if (color.Contains(A[0])) continue;
            ans -= DelQ.Take();
            ans += A[1];
            color.Add(A[0]);
            long cc = color.Count();
            max = Math.Max(ans + cc * cc, max);
            //Console.WriteLine(A[0] + " take");
        }
        Console.WriteLine(max);
    }
}

public class PriorityQueue<Tkey, Tvalue> where Tkey : IComparable
{
    private static List<Tkey> keys = new List<Tkey>();
    private static List<Tvalue> values = new List<Tvalue>();
    private int size = 0;
    private static bool Descending;
    private static int Compare(Tkey a, Tkey b) { return (Descending ? a.CompareTo(b) : b.CompareTo(a)); }

    public PriorityQueue(bool b = true) { Clear(); Descending = b; }
    public int Count() { return size; }
    public void Clear() { keys = new List<Tkey>(); values = new List<Tvalue>(); size = 0; }
    public void Add(Tkey e, Tvalue v)
    {
        keys.Add(e);
        values.Add(v);
        int x = size;
        size += 1;
        while (x != 0)
        {
            int par = (x % 2 == 0 ? x - 2 : x - 1) / 2;
            if (Compare(keys[par], e) <= 0) break;
            Tkey a = keys[x]; keys[x] = keys[par]; keys[par] = a;
            Tvalue b = values[x]; values[x] = values[par]; values[par] = b;
            x = par;
        }
    }
    public void Poll()
    {
        Tkey k = keys[size - 1];
        Tvalue v = values[size - 1];
        int x = 0;
        size--;
        if (size == 0) { Clear(); return; }
        keys.RemoveAt(size);
        values.RemoveAt(size);
        while (true)
        {
            int l = x * 2 + 1;
            int r = x * 2 + 2;
            if (size - 1 < l) break;
            int y = 0;
            if (size - 1 == l) { y = l; }
            else if (Compare(keys[l], keys[r]) == 1) { y = r; }
            else { y = l; }
            if (Compare(keys[y], k) > 0) break;
            keys[x] = keys[y];
            values[x] = values[y];
            x = y;
        }
        keys[x] = k;
        values[x] = v;
    }
    public Tvalue Take() { Tvalue ret = values[0]; Poll(); return ret; }
    public Tvalue Peek() { return values[0]; }
    public void Debug()
    {
        Console.Write("key   : ");
        foreach (var k in keys) Console.Write(k + " ");
        Console.WriteLine();
        Console.Write("value : ");
        foreach (var k in values) Console.Write(k + " ");
        Console.WriteLine();
    }
}

public class Input
{
    private static Queue<string> queue = new Queue<string>();
    private static void Confirm() { if (queue.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) queue.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(queue.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(queue.Dequeue()); }
    public static string NextString() { Confirm(); return queue.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(queue.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}