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: Runtime Error)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using static ABC116D.Input;

namespace ABC116D
{
    static class Input
    {
        /// <summary>
        /// 1行の入力をTに応じてリストに変換する関数を返す
        /// </summary>
        static Func<string, List<T>> Cast<T>() => _ => _.Split(' ').Select(Convert<T>()).ToList();

        /// <summary>
        /// 1行の入力をTに応じて変換する関数を返す
        /// </summary>
        static Func<string, T> Convert<T>()
        {
            Type t = typeof(T);
            if (t == typeof(string)) return _ => (T) (object) _;
            if (t == typeof(int)) return _ => (T) (object) int.Parse(_);
            if (t == typeof(long)) return _ => (T) (object) long.Parse(_);
            if (t == typeof(double)) return _ => (T) (object) double.Parse(_);
            if (t == typeof(List<string>)) return _ => (T) (object) Cast<string>()(_);
            if (t == typeof(List<int>)) return _ => (T) (object) Cast<int>()(_);
            if (t == typeof(List<long>)) return _ => (T) (object) Cast<long>()(_);
            if (t == typeof(List<double>)) return _ => (T) (object) Cast<double>()(_);

            throw new NotSupportedException(t + "is not supported.");
        }

        static string String() => Console.ReadLine();

        static List<string> String(long rowNumber) => new bool[rowNumber].Select(_ => String()).ToList();

        /// <summary>
        /// 1行の値の入力
        /// </summary>
        public static void @in<T>(out T a) => a = Convert<List<T>>()(String())[0];

        public static void @in<T>(out T a1, out T a2)
        {
            var v = Convert<List<T>>()(String());
            a1 = v[0];
            a2 = v[1];
        }

        public static void @in<T>(out T a1, out T a2, out T a3)
        {
            var v = Convert<List<T>>()(String());
            a1 = v[0];
            a2 = v[1];
            a3 = v[2];
        }

        public static void @in<T>(out T a1, out T a2, out T a3, out T a4)
        {
            var v = Convert<List<T>>()(String());
            a1 = v[0];
            a2 = v[1];
            a3 = v[2];
            a4 = v[3];
        }

        public static void @in<T>(out T a1, out T a2, out T a3, out T a4, out T a5)
        {
            var v = Convert<List<T>>()(String());
            a1 = v[0];
            a2 = v[1];
            a3 = v[2];
            a4 = v[3];
            a5 = v[4];
        }

        public static void @in<T>(out T a1, out T a2, out T a3, out T a4, out T a5, out T a6)
        {
            var v = Convert<List<T>>()(String());
            a1 = v[0];
            a2 = v[1];
            a3 = v[2];
            a4 = v[3];
            a5 = v[4];
            a6 = v[5];
        }

        /// <summary>
        /// 複数行の値の入力
        /// </summary>
        public static void @in<T>(long rowNumber, out List<T> l) => l = String(rowNumber).Select(Convert<T>()).ToList();

        public static void @in<T>(long rowNumber, out List<T> l1, out List<T> l2)
        {
            l1 = new List<T>();
            l2 = new List<T>();
            foreach (List<T> l in String(rowNumber).Select(Convert<List<T>>()))
            {
                l1.Add(l[0]);
                l2.Add(l[1]);
            }
        }

        public static void @in<T>(long rowNumber, out List<T> l1, out List<T> l2, out List<T> l3)
        {
            l1 = new List<T>();
            l2 = new List<T>();
            l3 = new List<T>();
            foreach (List<T> l in String(rowNumber).Select(Convert<List<T>>()))
            {
                l1.Add(l[0]);
                l2.Add(l[1]);
                l3.Add(l[2]);
            }
        }

        public static void @in<T>(long rowNumber, out List<T> l1, out List<T> l2, out List<T> l3, out List<T> l4)
        {
            l1 = new List<T>();
            l2 = new List<T>();
            l3 = new List<T>();
            l4 = new List<T>();
            foreach (List<T> l in String(rowNumber).Select(Convert<List<T>>()))
            {
                l1.Add(l[0]);
                l2.Add(l[1]);
                l3.Add(l[2]);
                l4.Add(l[3]);
            }
        }

        /// <summary>
        /// 1行に書かれた複数の値の入力
        /// </summary>
        public static void @in<T>(out List<T> lArr) => lArr = Convert<List<T>>()(String());

        /// <summary>
        /// h行の行列の入力
        /// </summary>
        public static void @in<T>(long h, out List<List<T>> map) => map = String(h).Select(Convert<List<T>>()).ToList();
    }

    class Program
    {
        public static void Main(string[] args)
        {
            StreamWriter streamWriter = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(streamWriter);
            new Solver().Solve();
            Console.Out.Flush();
        }

        public static void Debug()
        {
            new Solver().Solve();
        }
    }

    class Solver
    {
        private long N;
        private long K;
        private List<long> t;
        private List<long> d;

        public void Solve()
        {
            @in(out N, out K);
            @in(N, out t, out d);
            List<Pair> first = new List<Pair>();
            List<Pair> second = new List<Pair>();
            HashSet<long> seen = new HashSet<long>();
            for (int i = 0; i < N; i++)
            {
                if (seen.Contains(t[i]))
                {
                    second.Add(new Pair(t[i], d[i], i));
                }
                else
                {
                    first.Add(new Pair(t[i], d[i], i));
                    seen.Add(t[i]);
                }
            }

            first.Sort(new PairComperator());
            second.Sort(new PairComperator());

            long ans = 0;
            long sum = 0;
            int fIndex = 0;
            int sIndex = 0;
            //K種類から1種類の寿司を食べる
            for (long i = K; i >= 0; i--)
            {
                //寿司がたりない
                if (first.Count < K)
                {
                    continue;
                }

                if (first.Count == i)
                {
                    sum = first.Sum(_ => _.B);
                    ans = i * i + sum;
                    fIndex = first.Count - 1;
                    continue;
                }

                sum = sum - first[fIndex].B + second[sIndex].B;
                ans = Math.Max(ans, sum + i * i);
                sIndex++;
                fIndex--;
                if (sIndex >= second.Count)
                {
                    break;
                }
            }

            Console.WriteLine(ans);
        }
    }

    /// <summary>
    /// 値のペア ソート/出力用のindexも持つ
    /// </summary>
    class Pair
    {
        public long A;
        public long B;
        public long I;

        public Pair(long a, long b, long i)
        {
            A = a;
            B = b;
            I = i;
        }

        public override string ToString()
        {
            return "i: " + I + "  A: " + A + "  B: " + B;
        }
    }

    class PairComperator : IComparer<Pair>
    {
        int IComparer<Pair>.Compare(Pair a, Pair b)
        {
            return (int) b.B - (int) a.B;
        }
    }
}