Problem:
Score : 400 points

Problem Statement

You have N items and a bag of strength W.
The i-th item has a weight of w_i and a value of v_i.

You will select some of the items and put them in the bag.
Here, the total weight of the selected items needs to be at most W.

Your objective is to maximize the total value of the selected items.

Constraints

1 ≤ N ≤ 100

1 ≤ W ≤ 10^9

1 ≤ w_i ≤ 10^9

For each i = 2,3,...,N, w_1 ≤ w_i ≤ w_1 + 3.

1 ≤ v_i ≤ 10^7

W, each w_i and v_i are integers.

Input

Input is given from Standard Input in the following format:

N W
w_1 v_1
w_2 v_2
:
w_N v_N

Output

Print the maximum possible total value of the selected items.

Sample Input 1

4 6
2 1
3 4
4 10
3 4

Sample Output 1

11

The first and third items should be selected.

Sample Input 2

4 6
2 1
3 7
4 10
3 6

Sample Output 2

13

The second and fourth items should be selected.

Sample Input 3

4 10
1 100
1 100
1 100
1 100

Sample Output 3

400

You can take everything.

Sample Input 4

4 1
10 100
10 100
10 100
10 100

Sample Output 4

0

You can take nothing.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.IO;
using System.Collections.Generic;
using System.Linq;

namespace ARC073D
{
    public class WeightValuePair
    {
        public long Weight { get; }
        public long Value { get; }

        public WeightValuePair(long weight, long value)
        {
            Weight = weight;
            Value = value;
        }
    }

    public class Program
    {
        WeightValuePair[][] G;
        int N;
        long W;

        void Solve(StreamScanner ss, StreamWriter sw)
        {
            //---------------------------------
            N = ss.Next(int.Parse);
            W = ss.Next(long.Parse);
            G = ss.Next(long.Parse, 2, N)
                .Select(a => new WeightValuePair(a[0], a[1]))
                .GroupBy(wv => wv.Weight)
                .OrderBy(g => g.Key)
                .Select(g => g.OrderByDescending(wv => wv.Value).ToArray())
                .ToArray();

            sw.WriteLine(GetAns(0, 0, 0));
            //---------------------------------
        }

        long GetAns(int num, long totalWeight, long totalValue)
        {
            if (num >= G.Length)
            {
                return totalWeight > W ? long.MinValue : totalValue;
            }

            var ret = long.MinValue;

            for (var i = 0; i <= G[num].Length; i++)
            {
                if (i != 0)
                {
                    totalWeight += G[num][i - 1].Weight;
                    totalValue += G[num][i - 1].Value;
                }
                ret = Math.Max(ret, GetAns(num + 1, totalWeight, totalValue));
            }

            return ret;
        }

        static void Main()
        {
            var ss = new StreamScanner(new StreamReader(Console.OpenStandardInput()));
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            new Program().Solve(ss, sw);
            sw.Flush();
        }

        static readonly Func<string, string> String = s => s;
    }

    public class StreamScanner
    {
        static readonly char[] Sep = { ' ' };
        readonly Queue<string> buffer = new Queue<string>();
        readonly TextReader textReader;

        public StreamScanner(TextReader textReader)
        {
            this.textReader = textReader;
        }

        public T Next<T>(Func<string, T> parser)
        {
            if (buffer.Count != 0) return parser(buffer.Dequeue());
            var nextStrings = textReader.ReadLine().Split(Sep, StringSplitOptions.RemoveEmptyEntries);
            foreach (var nextString in nextStrings) buffer.Enqueue(nextString);
            return Next(parser);
        }

        public T[] Next<T>(Func<string, T> parser, int x)
        {
            var ret = new T[x];
            for (var i = 0; i < x; ++i) ret[i] = Next(parser);
            return ret;
        }

        public T[][] Next<T>(Func<string, T> parser, int x, int y)
        {
            var ret = new T[y][];
            for (var i = 0; i < y; ++i) ret[i] = Next(parser, x);
            return ret;
        }
    }
}