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

public class Prog
{
    private const int INF = 1000000007;
    private const long INFINITY = 9223372036854775807;
    public static void Main()
    {
        //w1から3しか重さが違わない
        int N = NextInt();
        int W = NextInt();
        int[] w = new int[N];
        int[] v = new int[N];
        int w1 = NextInt();
        w[0] = 0;
        v[0] = NextInt();
        for (int i = 1; i < N; i++)
        {
            w[i] = NextInt() - w1;
            v[i] = NextInt();
        }
        // i 個目の要素までの解 , 適当に , w1に相当する重さが何個あるか
        long[,,] dp = new long[N + 1, 500, 500];
        for (int i = 0; i <= N; i++)
            for (int j = 0; j < 500; j++)
                for (int k = 0; k < 500; k++) dp[i, j, k] = -INF;
        dp[0, 0, 0] = 0;
        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < 500; j++)
            {
                for (int k = 0; k < 500; k++)
                {
                    if (dp[i, j, k] == -INF) continue;
                    dp[i + 1, j, k] = dp[i, j, k];
                    if ((k + 1) * w1 + j + w[i] > W) break;
                    dp[i + 1, j + w[i], k + 1] = Math.Max(dp[i, j + w[i], k + 1], dp[i, j, k] + v[i]);
                }
            }
        }

        long ans = 0;
        for (int j = 0; j < 500; j++)
            for (int k = 0; k < 500; k++) ans = Math.Max(dp[N, j, k], ans);
        Console.WriteLine(ans);
    }
}

public class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}