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.Collections.Generic;
using System.Linq;
using System.Globalization;
using System.IO;
using CodeChallenges;
using System.Diagnostics;

namespace CodeChallenges.Boilerplate.IO
{
    #region helpers
    class FormattedStreamWriter : StreamWriter { public FormattedStreamWriter(Stream stream) : base(stream) { } public FormattedStreamWriter(string filePath) : base(filePath) { } public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } } }
    static class IOExtensions
    {
        public static string ReadString(this StreamReader reader) { return reader.ReadToken(); }
        public static string[] ReadStringArray(this StreamReader reader, int n) { var array = new string[n]; for (int i = 0; i < n; ++i) { array[i] = reader.ReadToken(); } return array; }
        public static int ReadInt(this StreamReader reader) { return int.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); }
        public static int[] ReadIntArray(this StreamReader reader, int n) { var array = new int[n]; for (int i = 0; i < n; ++i) { array[i] = int.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); } return array; }
        public static uint ReadUnsignedInt(this StreamReader reader) { return uint.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); }
        public static long ReadLong(this StreamReader reader) { return long.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); }
        public static long[] ReadLongArray(this StreamReader reader, int n) { var array = new long[n]; for (int i = 0; i < n; ++i) { array[i] = long.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); } return array; }
        public static ulong ReadUnsignedLong(this StreamReader reader) { return ulong.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); }
        public static double ReadDouble(this StreamReader reader) { return double.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); }
        public static double[] ReadDoubleArray(this StreamReader reader, int n) { var array = new double[n]; for (int i = 0; i < n; ++i) { array[i] = double.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); } return array; }
        public static decimal ReadDecimal(this StreamReader reader) { return decimal.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); }
        public static decimal[] ReadDecimalArray(this StreamReader reader, int n) { var array = new decimal[n]; for (int i = 0; i < n; ++i) { array[i] = decimal.Parse(reader.ReadToken(), CultureInfo.InvariantCulture); } return array; }
        public static void ResetBuffer() { buffer = new Queue<string>(1000); }
        static Queue<string> buffer = new Queue<string>(1000);
        static string ReadToken(this StreamReader reader) { while (buffer.Count == 0) { reader.ReadLine().Split(new[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries).ToList().ForEach((t) => { buffer.Enqueue(t); }); } return buffer.Dequeue(); }
    }
    #endregion
}

#region launch
class Program
{
    static void Main(string[] args)
    {
#if SOLVER_ATWORKSPACE
        var run = true; var outputFile = "output.txt"; var inputFile = "input.txt";
        switch (args[0])
        {
            case "g": run = false; outputFile = "input.txt"; inputFile = "output.txt"; break;
            case "r":
            default: run = true; inputFile = "input.txt"; outputFile = "output.txt"; break;
        }
#endif

        using (var writer = new CodeChallenges.Boilerplate.IO.FormattedStreamWriter(
#if SOLVER_ATWORKSPACE
outputFile
#else
            Console.OpenStandardOutput()
#endif
))
        {
            using (var reader = new StreamReader(
#if SOLVER_ATWORKSPACE
inputFile
#else 
            Console.OpenStandardInput()
#endif
))
            {
#if SOLVER_ATWORKSPACE
                var stopw = new Stopwatch(); stopw.Start();
#endif
#if SOLVER_ATWORKSPACE
                if (run) new Solver(reader, writer).Do(); else new Generator(reader, writer).Create();

#else
                new Solver(reader, writer).Do();
#endif
#if SOLVER_ATWORKSPACE
                stopw.Stop(); writer.WriteLine("> {0}ms", stopw.ElapsedMilliseconds);
#endif
            }
        }
    }
}
#endregion

namespace CodeChallenges
{
    using CodeChallenges.Boilerplate.IO;

    public class Solver
    {
        private readonly StreamReader reader;
        private readonly StreamWriter writer;

        public Solver(StreamReader reader, StreamWriter writer)
        {
            this.reader = reader;
            this.writer = writer;
        }        

        //public int Solve(int W, int K, int N)
        //{
        //    if (K == 0)
        //        return 0;
        //    if (dim[N][K][W] > 0)
        //        return dim[N][K][W] - 1;
        //    var one = K < N ? Solve(W, K, N - 1): 0;
        //    var two = (W >= w[N - 1])? (v[N - 1] + Solve(W - w[N - 1], K - 1, N - 1)): 0;
        //    dim[N][K][W] = Math.Max(one, two) + 1;
        //    return dim[N][K][W] - 1;
        //}

        public void Do()
        {
            const int DELTA = 3;
            int N = reader.ReadInt();
            int W = reader.ReadInt();
            int[][][] dim = new int[N + 1][][];
            int[] w = new int[N];
            int[] v = new int[N];
            for (int i = 0; i < N; ++i)
            {
                w[i] = reader.ReadInt();
                v[i] = reader.ReadInt();
            }
            var w0 = w[0];
            for (int i = 0; i <= N; ++i)
            {
                dim[i] = new int[N + 1][];
                for (int j = 0; j <= N; ++j)
                {
                    dim[i][j] = new int[DELTA * N + 1];
                    for (int k = 0; k <= DELTA * N; ++k)
                        dim[i][j][k] = int.MinValue;
                }
            }            
            for (int i = 0; i <= N; ++i)
            {
                for (int k = 0; k <= DELTA * N; ++k)
                    dim[i][0][k] = 0;
                if (i > 0)
                    w[i - 1] -= w0;
                for (int j = 1; j <= i; ++j)
                    for (int k = 0; k <= DELTA * N; ++k)
                    {
                        if (k >= w[i - 1])
                            dim[i][j][k] = Math.Max(dim[i][j][k], v[i - 1] + dim[i - 1][j - 1][k - w[i - 1]]);
                        if (i > j)
                            dim[i][j][k] = Math.Max(dim[i][j][k], dim[i - 1][j][k]);
                    }
            }
            int total = 0;
            for (int ii = 1; ii <= N; ++ii)
                if (W - 1L * ii * w0 >= 0)
                {
                    var WN = Math.Min(W - ii * w0, ii * DELTA);
                    total = Math.Max(total, dim[N][ii][WN]);
                }
            writer.WriteLine(total);
        }
    }
}