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 JAVA (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        KnapsackAizu1 solver = new KnapsackAizu1();
        solver.solve(1, in, out);
        out.close();
    }

    static class KnapsackAizu1 {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            int w = in.nextInt();
            int[] vs = new int[n];
            int[] ws = new int[n];

            for (int i = 0; i < n; i++) {
                vs[i] = in.nextInt();
                ws[i] = in.nextInt();
            }

            int[] dp = new int[w + 1];
            for (int i = 1; i < w + 1; i++) {
                for (int j = 0; j < n; j++) {
                    if (i >= ws[j]) {
                        dp[i] = Math.max(dp[i], vs[j] + dp[i - ws[j]]);
                    }
                }
            }

            out.printf("%d\n", dp[w]);
        }

    }
}