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: Wrong Answer)

#if DEBUG
using Microsoft.VisualStudio.TestTools.UnitTesting;
#endif
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Contest
{
    class Program
    {
        public static IO.StreamScanner scanner = new IO.StreamScanner(Console.OpenStandardInput());

        static void Main(string[] args)
        {
            var n = scanner.Integer();
            var k = scanner.Long();
            var td = new List<Tuple<long, long>>();
            for (int i = 0; i < n; i++) td.Add(new Tuple<long, long>(scanner.Long(), scanner.Long()));

            var ans = GetAns(n, k, td);
            IO.Printer.Out.WriteLine(ans);
            IO.Printer.Out.Flush();
        }

        public static long GetAns(int n, long k, List<Tuple<long, long>> td)
        {
            // type => deliciousness
            var dict = new Dictionary<long, List<long>>();
            foreach(var tpl in td)
            {
                if (!dict.ContainsKey(tpl.Item1)) dict[tpl.Item1] = new List<long>();
                dict[tpl.Item1].Add(tpl.Item2);
            }
            var indices = new Dictionary<long, int>();
            foreach (var key in dict.Keys)
            {
                dict[key].Sort();
                indices[key] = dict[key].Count() - 1;
            }

            var cnt = 0;
            var selectedTypes = new HashSet<long>();
            var deliciousSum = 0L;

            while(cnt < k)
            {
                var next = -1L;
                var max = long.MinValue;

                foreach(var key in dict.Keys)
                {
                    if (indices[key] == -1) continue;
                    var nextDel = deliciousSum + dict[key][indices[key]];
                    var nextTypes = selectedTypes.Count() + (selectedTypes.Contains(key) ? 0 : 1);
                    var nextScore = nextDel + nextTypes * nextTypes;

                    if (max < nextScore)
                    {
                        next = key;
                        max = nextScore;
                    }
                }

                selectedTypes.Add(next);
                deliciousSum += dict[next][indices[next]];
                indices[next]--;

                cnt++;
            }

            return deliciousSum + selectedTypes.Count() * selectedTypes.Count();
        }        
    }

#if DEBUG
    [TestClass]
    public class Test
    {
        [TestMethod]
        public void Test1()
        {
            var n = 5;
            var k = 3;
            var td = new List<Tuple<long, long>>
            {
                new Tuple<long, long>(1, 9),
                new Tuple<long, long>(1, 7),
                new Tuple<long, long>(2, 6),
                new Tuple<long, long>(2, 5),
                new Tuple<long, long>(3, 1),
            };
            var exp = 26;
            var ans = Program.GetAns(n, k, td);
            Assert.AreEqual(exp, ans);
        }


        bool IsEq(IEnumerable<char> l1, IEnumerable<char> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for (int i = 0; i > l1.Count(); i++)
            {
                if (l1.ElementAt(i) != l2.ElementAt(i)) return false;
            }
            return true;
        }

        bool IsEq(IEnumerable<int> l1, IEnumerable<int> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for(int i=0; i>l1.Count(); i++)
            {
                if (l1.ElementAt(i) != l2.ElementAt(i)) return false;
            }
            return true;
        }

        bool IsEq(IEnumerable<long> l1, IEnumerable<long> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for (int i = 0; i > l1.Count(); i++)
            {
                if (l1.ElementAt(i) != l2.ElementAt(i)) return false;
            }
            return true;
        }

        bool IsEq(IEnumerable<double> l1, IEnumerable<double> l2)
        {
            if (l1.Count() != l2.Count()) return false;
            for (int i = 0; i > l1.Count(); i++)
            {
                if (l1.ElementAt(i) != l2.ElementAt(i)) return false;
            }
            return true;
        }

        bool IsEq(double d1, double d2)
        {
            return Math.Abs(d2 - d1) < 1E10;
        }

    }
#endif

    namespace IO
    {
        using System.IO;
        using System.Text;
        using System.Globalization;

        public class Printer : StreamWriter
        {
            static Printer()
            {
                Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false };
            }

            public static Printer Out { get; set; }

            public override IFormatProvider FormatProvider
            {
                get { return CultureInfo.InvariantCulture; }
            }

            public Printer(Stream stream)
                : base(stream, new UTF8Encoding(false, true))
            {
            }

            public Printer(Stream stream, Encoding encoding)
                : base(stream, encoding)
            {
            }

            public void Write<T>(string format, T[] source)
            {
                base.Write(format, source.OfType<object>().ToArray());
            }

            public void WriteLine<T>(string format, T[] source)
            {
                base.WriteLine(format, source.OfType<object>().ToArray());
            }
        }

        public class StreamScanner
        {
            public StreamScanner(Stream stream)
            {
                str = stream;
            }

            public readonly Stream str;
            private readonly byte[] buf = new byte[1024];
            private int len, ptr;
            public bool isEof;

            public bool IsEndOfStream
            {
                get { return isEof; }
            }

            private byte read()
            {
                if (isEof) return 0;
                if (ptr < len) return buf[ptr++];
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) > 0) return buf[ptr++];
                isEof = true;
                return 0;
            }

            public char Char()
            {
                byte b;
                do b = read(); while ((b < 33 || 126 < b) && !isEof);
                return (char)b;
            }

            public string Scan()
            {
                var sb = new StringBuilder();
                for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                    sb.Append(b);
                return sb.ToString();
            }

            public string ScanLine()
            {
                var sb = new StringBuilder();
                for (var b = Char(); b != '\n'; b = (char)read())
                    if (b == 0) break;
                    else if (b != '\r') sb.Append(b);
                return sb.ToString();
            }

            public long Long()
            {
                if (isEof) return long.MinValue;
                long ret = 0;
                byte b;
                var ng = false;
                do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b));
                if (b == 0) return long.MinValue;
                if (b == '-')
                {
                    ng = true;
                    b = read();
                }
                for (; ; b = read())
                {
                    if (b < '0' || '9' < b)
                        return ng ? -ret : ret;
                    ret = ret * 10 + b - '0';
                }
            }

            public int Integer()
            {
                return (isEof) ? int.MinValue : (int)Long();
            }

            public double Double()
            {
                var s = Scan();
                return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN;
            }

            static T[] enumerate<T>(int n, Func<T> f)
            {
                var a = new T[n];
                for (int i = 0; i < n; ++i) a[i] = f();
                return a;
            }

            public char[] Char(int n)
            {
                return enumerate(n, Char);
            }

            public string[] Scan(int n)
            {
                return enumerate(n, Scan);
            }

            public double[] Double(int n)
            {
                return enumerate(n, Double);
            }

            public int[] Integer(int n)
            {
                return enumerate(n, Integer);
            }

            public long[] Long(int n)
            {
                return enumerate(n, Long);
            }
        }
    }
}