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: Accepted)

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

/*
?????°??¶????????????????????¶??????
*/
public class Program{
    public static void Main(){
        var input = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var N = input[0];
        var W = input[1];
        var Product_Value = new int[N];
        var Product_Weight = new int[N];
        for(int i=0; i<N; i++){
            var info = Console.ReadLine().Split().Select(int.Parse).ToArray();
            Product_Value[i] = info[0];
            Product_Weight[i] = info[1];
        }
        //??¶????????????????????§??????????????¨?????????
        var dp = new int[N+1, W+1];
        
        for(int i=1; i<N+1; i++){
            for(int j=0; j<W+1; j++){
                //?????¨??????????????\????????????????????¢???????¶??????????????????´????????????????????????????????????
                //j???????????¨????????????????¨??????§
                if(j<Product_Weight[i-1]){
                    dp[i, j] = dp[i-1, j];
                }else{
                    dp[i, j] = Math.Max(dp[i-1, j], dp[i, j-Product_Weight[i-1]]+Product_Value[i-1]);
                }
            }
        }
        
        //one dimensional array version
        /*
        var dp2 = new int[W+1];
        for(int i=1; i<N+1; i++){
            for(int j=Product_Weight[i-1]; j<W+1; j++){
                dp2[j] = Math.Max(dp2[j-1], dp2[j-Product_Weight[i-1]]+Product_Value[i-1]);
            }
        }
        */
        Console.WriteLine(dp[N, W]);
    }
}