Problem:
Knapsack Problem

You have N kinds of items that you want to put them into a knapsack. Item i has value vi and weight wi.

You want to find a subset of items to put such that:

The total value of the items is as large as possible.

The items have combined weight at most W, that is capacity of the knapsack.

You can select as many items as possible into a knapsack for each kind.

Find the maximum total value of items in the knapsack.

Input

N W
v1 w1
v2 w2
:
vN wN

The first line consists of the integers N and W. In the following lines, the value and weight of the i-th item are given.

Output

Print the maximum total values of the items in a line.

Constraints

1 ≤ N ≤ 100

1 ≤ vi ≤ 1000

1 ≤ wi ≤ 1000

1 ≤ W ≤ 10000

Sample Input 1

4 8
4 2
5 2
2 1
8 3

Sample Output 1

21

Sample Input 2

2 20
5 9
4 10

Sample Output 2

10

Sample Input 3

3 9
2 1
3 1
5 2

Sample Output 3

27

Solution in C# (judge verdict: Time Limit Exceeded)

using System;

public class hello
{
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var n = int.Parse(line[0]);
        var wmax = int.Parse(line[1]);
        var p = new int[n];
        var w = new int[n];
        for (int i = 0; i < n; i++)
        {
            string[] line2 = Console.ReadLine().Trim().Split(' ');
            p[i] = int.Parse(line2[0]);
            w[i] = int.Parse(line2[1]);
        }
        var dp = new int[n + 1, wmax + 1];
        for (int i = 0; i < n + 1; i++)
            for (int j = 0; j < wmax + 1; j++)
                dp[i, j] = -1;
        var ans = Rec(0, wmax, n, w, p,dp);
        Console.WriteLine(ans);
    }
    public static int Rec(int i, int j, int n, int[] w, int[] p ,int[,] dp)
    {
        if (dp[i, j] != -1) return dp[i, j];
        if (i == n) return 0;
        if (j < w[i])
        {
            var t1 = Rec(i + 1, j, n, w, p ,dp);
            return t1;
        }
        else
        {
            var comp1 = Rec(i + 1, j, n, w, p ,dp);
            if (dp[i + 1, j] == -1) dp[i + 1, j] = comp1;
            var tempmax = comp1;
            for (int k = 1; j >= w[i] * k; k++)
            {
                var comp2 = Rec(i + 1, j - w[i] * k, n, w, p ,dp) + p[i] * k;
                if (dp[i + 1, j - w[i] * k] == -1) dp[i + 1, j - w[i] * k] = comp2 - p[i] * k;
                if (comp2 > tempmax) tempmax = comp2;
            }
            return tempmax;
        }
    }
}