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: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Text;

namespace Program
{
    public class ARC073D
    {
        static public void Main(string[] args)
        {
            var N = NextInt;
            var W = NextInt;
            var wAry = new int[N];
            var vAry = new int[N];
            var firstW = NextInt;
            wAry[0] = 1;
            vAry[0] = NextInt;
            for (int i = 1; i < N; ++i)
            {
                wAry[i] = NextInt - firstW + 1;
                vAry[i] = NextInt;
            }
            var dp = new ulong[N + 1][];
            var dpc = new int[N + 1][];
            for (int i = 0; i <= N; ++i)
            {
                dp[i] = new ulong[wAry.Sum() + 1];
                dpc[i] = new int[wAry.Sum() + 1];
            }
            var sumW = 0;
            for (int i = 1; i <= N; ++i)
            {
                var w = wAry[i - 1];
                var v = (ulong)vAry[i - 1];
                sumW += w;
                for (int j = 0; j <= sumW; ++j)
                {
                    if (j >= w)
                    {
                        if (dp[i - 1][j] > dp[i - 1][j - w] + v)
                        {
                            dp[i][j] = dp[i - 1][j];
                            dpc[i][j] = dpc[i - 1][j];
                        }
                        else
                        {
                            dp[i][j] = dp[i - 1][j - w] + v;
                            dpc[i][j] = dpc[i - 1][j - w] + 1;
                        }
                    }
                    else
                    {
                        dp[i][j] = dp[i - 1][j];
                        dpc[i][j] = dpc[i - 1][j];
                    }
                }
            }

            var ans = (ulong)0;
            for (int i = 1; i <= N; ++i)
            {
                for (int j = 0; j <= sumW; ++j)
                {
                    if (W - dpc[i][j] * (firstW - 1) >= j && ans < dp[i][j])
                    {
                        ans = dp[i][j];
                    }
                }
            }

            Console.WriteLine(ans);
        }

        static class Console_
        {
            private static Queue<string> param = new Queue<string>();
            public static string NextString()
            {
                if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item);
                return param.Dequeue();
            }
        }
        static int NextInt => int.Parse(Console_.NextString());
        static long NextLong => long.Parse(Console_.NextString());
        static string NextString => Console_.NextString();

        static IEnumerable<long> Prime(long x)
        {
            if (x < 2) yield break;
            yield return 2;
            var halfx = x / 2;
            var table = new bool[halfx + 1];
            var max = (long)(Math.Sqrt(x) / 2);
            for (long i = 1; i <= max; ++i)
            {
                if (table[i]) continue;
                var add = 2 * i + 1;
                yield return add;
                for (long j = 2 * i * (i + 1); j <= halfx; j += add) table[j] = true;
            }
            for (long i = max + 1; i <= halfx; ++i) if (!table[i]) yield return 2 * i + 1;
        }
        static IEnumerable<long> Divisor(long x)
        {
            if (x < 1) yield break;
            var max = (long)Math.Sqrt(x);
            for (long i = 1; i < max; ++i)
            {
                if (x % i != 0) continue;
                yield return i;
                if (i != x / i) yield return x / i;
            }
        }
        static long GCD(long a, long b)
        {
            long tmpa = a, tmpb = b;
            while (tmpb > 0) { var tmp = tmpb; tmpb = tmpa % tmpb; tmpa = tmp; }
            return tmpa;
        }
    }
}