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 System.IO;
//using System.Text;
//using System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
//using System.Numerics;
//using static System.Math;
using pair = Pair<long, int>;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    readonly Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;
    void chmax<T>(ref T a, T b) where T : IComparable<T> { a = a.CompareTo(b) < 0 ? b : a; }
    void chmin<T>(ref T a, T b) where T : IComparable<T> { a = a.CompareTo(b) < 0 ? a : b; }

    void solve()
    {
        int N = cin.nextint;
        int K = cin.nextint;

        var used = new bool[N];
        var gomi = new PriorityQueue<long>(-1);
        var ans = 0L;

        var tmp = 0L;
        var net = 0L;

        var P = new pair[N];
        for (int i = 0; i < N; i++)
        {
            var t = cin.nextint - 1;
            var d = cin.nextlong;
            P[i] = new pair(d, t);
        }
        Array.Sort(P);
        Array.Reverse(P);

        for (int i = 0; i < N; i++)
        {
            var v = P[i].f;
            var u = P[i].s;
            if (i < K)
            {
                tmp += v;
                if (used[u])
                {
                    gomi.Enqueue(v);
                }
                else
                {
                    used[u] = true;
                    net++;
                }
            }
            else
            {
                if (!gomi.Any())
                {
                    break;
                }
                if (used[u])
                {
                    continue;
                }

                var e = gomi.Dequeue();
                tmp = tmp - e + v;
                used[u] = true;
                net++;
            }
            chmax(ref ans, net * net + tmp);
        }
        WriteLine(ans);
    }

}


class Pair<T, U> : IComparable<Pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T f;
    public U s;
    public Pair(T f, U s)
    {
        this.f = f;
        this.s = s;
    }
    public int CompareTo(Pair<T, U> a)
    {
        return f.CompareTo(a.f) != 0 ? f.CompareTo(a.f) : s.CompareTo(a.s);
    }
    public override string ToString()
    {
        return f + " " + s;
    }
}
class PriorityQueue<T> where T : IComparable<T>
{
    List<T> heap; int size;
    readonly int cmp = 1;
    int Compare(T x, T y) { return y.CompareTo(x); }
    public PriorityQueue() { heap = new List<T>(); }
    public PriorityQueue(int k) { heap = new List<T>(); cmp = k; }
    public void Enqueue(T x)
    {
        heap.Add(x);
        int i = size++;
        while (i > 0)
        {
            int p = (i - 1) >> 1;
            if (Compare(heap[p], x) * cmp <= 0) break;
            heap[i] = heap[p]; i = p;
        }
        heap[i] = x;
    }
    public T Dequeue()
    {
        T ret = heap[0]; T x = heap[--size];
        int i = 0;
        while ((i << 1) + 1 < size)
        {
            int a = (i << 1) + 1; int b = (i << 1) + 2;
            if (b < size && Compare(heap[b], heap[a]) * cmp < 0) a = b;
            if (Compare(heap[a], x) * cmp >= 0) break;
            heap[i] = heap[a]; i = a;
        }
        heap[i] = x; heap.RemoveAt(size);
        return ret;
    }
    public int Count { get { return size; } }
    public bool Any() { return size > 0; }
    public T Peek() { return heap[0]; }
}
class Scanner
{
    string[] s; int i;
    readonly char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan { get { return ReadLine().Split(); } }
    public int[] scanint { get { return Array.ConvertAll(scan, int.Parse); } }
    public long[] scanlong { get { return Array.ConvertAll(scan, long.Parse); } }
    public double[] scandouble { get { return Array.ConvertAll(scan, double.Parse); } }
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint { get { return int.Parse(next); } }
    public long nextlong { get { return long.Parse(next); } }
    public double nextdouble { get { return double.Parse(next); } }
    public void join<T>(IEnumerable<T> values) { WriteLine(string.Join(" ", values)); }
}