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.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;

namespace AtCoder
{
	public class ABC
	{
		static int mod = 1000000007;  // 10^9+7

		static void Main(string[] args)
		{
			Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });


			//int n = int.Parse(Console.ReadLine());
			//string s = Console.ReadLine();
			int[] vs = Console.ReadLine().Split().Select(int.Parse).ToArray();
			int n = vs[0];
			int k = vs[1];
			PriorityQueue<Sushi> queue = new PriorityQueue<Sushi>((x, y) => y.value.CompareTo(x.value));
			for (int i = 0; i < n; i++) {
				vs = Console.ReadLine().Split().Select(int.Parse).ToArray();
				queue.Enqueue(new Sushi() { neta = vs[0], value = vs[1] });
			}

			HashSet<int> neta = new HashSet<int>();
			PriorityQueue<Sushi> sushi = new PriorityQueue<Sushi>((x, y) => x.value.CompareTo(y.value));
			long sum = 0, ans = 0;
			for (int i = 0; i < n; i++) {
				Sushi item = queue.Dequeue();
				if (i < k) {
					if (!neta.Contains(item.neta)) {
						neta.Add(item.neta);
					} else {
						sushi.Enqueue(item);
					}
					sum += item.value;
					ans = sum + (long)neta.Count * neta.Count;
					//System.Diagnostics.Debug.WriteLine($"({item.neta},{item.value}) {ans}={sum}+{neta.Count}^2");
				} else {
					if (!neta.Contains(item.neta)) {
						if (sushi.Count == 0) {
							break;
						}
						neta.Add(item.neta);
						sum += item.value;
						Sushi item2 = sushi.Dequeue();
						sum -= item2.value;
						ans = Math.Max(ans, sum + (long)neta.Count * neta.Count);
						//System.Diagnostics.Debug.WriteLine($"-({item2.neta},{item2.value})+({item.neta},{item.value}) {sum + neta.Count * neta.Count}={sum}+{neta.Count}^2");
					}
				}
			}
			Console.WriteLine(ans);


			Console.Out.Flush();
		}
	}

	public class Sushi
	{
		public int neta;
		public int value;
	}

	#region 優先度付きキュー PriorityQueue<T>
	public class PriorityQueue<T> // where T : IComparable
	{
		private readonly List<T> _Heap;
		private readonly Func<T, T, int> _Compare;

		public int Count { get { return _Heap.Count; } }

		public PriorityQueue() : this(Comparer<T>.Default.Compare) { }
		public PriorityQueue(bool reverse) : this((x, y) => Comparer<T>.Default.Compare(reverse ? y : x, reverse ? x : y)) { }
		public PriorityQueue(Comparer<T> comparer) : this(comparer.Compare) { }
		public PriorityQueue(Func<T, T, int> compare)
		{
			_Heap = new List<T>();
			_Compare = compare;
		}

		public void Enqueue(T item)
		{
			_Heap.Add(item);
			int i = _Heap.Count - 1;
			while (i > 0) {
				int p = (i - 1) / 2;
				if (_Compare(_Heap[p], item) <= 0) {
					break;
				}
				_Heap[i] = _Heap[p];
				i = p;
			}
			_Heap[i] = item;
		}

		public T Dequeue()
		{
			int size = _Heap.Count - 1;
			T ret = _Heap[0];
			T x = _Heap[size];
			int i = 0;
			while (i * 2 + 1 < size) {
				var a = i * 2 + 1;
				var b = i * 2 + 2;
				if (b < size && _Compare(_Heap[b], _Heap[a]) < 0) {
					a = b;
				}
				if (_Compare(_Heap[a], x) >= 0) {
					break;
				}
				_Heap[i] = _Heap[a];
				i = a;
			}
			_Heap[i] = x;
			_Heap.RemoveAt(size);
			return ret;
		}

		public T Peek()
		{
			return _Heap[0];
		}

		public void Clear()
		{
			_Heap.Clear();
		}

		public List<T>.Enumerator GetEnumerator()
		{
			return _Heap.GetEnumerator();
		}

		public override string ToString()
		{
			return string.Join(" ", _Heap);
		}
	}
	#endregion

}