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;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;


public class Pair
{
	public long T { get; private set; }
	public long D { get; private set; }

	public Pair(long t, long d)
	{
		T = t;
		D = d;
	}
}


public class D
{
	public static void Main()
	{
		int N = GetInt();
		int K = GetInt();
		List<Pair> pairs = new List<Pair>(N);
		for(int i = 0; i < N; i++)
			pairs.Add(new Pair(GetLong(), GetLong()));
		pairs.Sort((p,q) => (int)(q.D - p.D));

		bool[] usedNeta = new bool[N+1];
		PriorityQueue<long> nextRemove = new PriorityQueue<long>(N, 0);
		PriorityQueue<long> nextAdd = new PriorityQueue<long>(N, 1);
		
		long basePoint = 0;
		int x = 0;
		for(int i = 0; i < K; i++)
		{
			Pair pair = pairs[i];
			basePoint += pair.D;

			if(usedNeta[pair.T])
			{
				nextRemove.Push(pair.D);								
			}
			else
			{
				usedNeta[pair.T] = true;
				x++;
			}			
		}

		for(int i = K; i < N; i++)
		{
			Pair pair = pairs[i];
			if(usedNeta[pair.T])
				continue;

			usedNeta[pair.T] = true;
			nextAdd.Push(pair.D);
		}

		long[] f = new long[N+1];
		for(int i = 1; i <= N; i++)
			f[i] = long.MinValue;
		f[x] = basePoint;
		for(int a = x + 1; a <= N; a++)
		{
			if(nextRemove.Size == 0)
				break;
			if(nextAdd.Size == 0)
				break;

			basePoint -= nextRemove.Pop();
			basePoint += nextAdd.Pop();
			f[a] = basePoint;
		}

		long[] g = new long[N+1];
		long ans = long.MinValue;
		for(long i = x; i <= N; i++)
		{
			g[(int)i] = f[(int)i] + i * i;
			ans = Math.Max(ans, g[(int)i]);
		}
		Console.WriteLine(ans);		
	}
}



public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}


public class PriorityQueue<T> where T:IComparable<T>
{
	public long Size { get; private set; } = 0;
	public long MaxSize { get; private set; } = 0;
	private T[] m_heap;
	public int Type { get; private set; } = 0;  // 0: ascending
	
	public PriorityQueue(long maxSize, int type)
	{
		if(maxSize <= 0)
			throw new Exception();
		MaxSize = maxSize;
		m_heap = new T[maxSize];
		
		Type = type;
	}
	
	private int Compare(T x, T y)
	{
		return (Type == 0) ? x.CompareTo(y) : y.CompareTo(x);
	}
	
	public void Push(T x)
	{
		if(Size == MaxSize)
			throw new Exception("Queue is full.");
		
		long i = Size++;
		while(i > 0)
		{
			long p = (i - 1)/2;
			if(Compare(m_heap[p],x) <= 0)
				break;
			m_heap[i] = m_heap[p];
			i = p;			
		}
		m_heap[i] = x;		
	}
	
	public T Pop()
	{
		if(Size == 0)
			throw new Exception("Queue is empty.");
		
		T result = m_heap[0];
		T x = m_heap[--Size];
		long i = 0;
		while(i * 2 + 1 < Size)
		{
			long c1 = i * 2 + 1, c2 = i * 2 + 2;
			if(c2 < Size && Compare(m_heap[c2], m_heap[c1]) < 0)
				c1 = c2;
			if(Compare(m_heap[c1], x) >= 0)
				break;
			m_heap[i] = m_heap[c1];
			i = c1;
		}
		m_heap[i] = x;
		
		return result;		
	}	
}