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.IOException;
import java.io.InputStream;
import java.math.BigDecimal;
import java.util.*;
import java.util.function.IntFunction;
import java.util.function.Supplier;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.Stream;


public class Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner();
        int n=scanner.nextInt();
        int W=scanner.nextInt();
        int[] dp=new int[W+1];
        for(int i=1;i<=n;i++){
            int v=scanner.nextInt();
            int w=scanner.nextInt();
            for(int j=0;j<=W;j++){
                if(j<w){
                    dp[j]=dp[j];
                }else{
                    dp[j]=Math.max(dp[j],dp[j-w]+v);
                }
            }
            //put(Arrays.toString(dp[i]));
        }
        put(dp[W]);




    }

    public static int upper_bound(int[] a,int val){
        return upper_bound(a,0,a.length,val);
    }
    public static int upper_bound(int[] a,int l,int r,int val){
        if(r-l==1){
            if(a[l]>val) return l;
            return r;
        }
        int mid=(l+r)/2;
        if(a[mid]>val){
            return upper_bound(a,l,mid,val);
        }else{
            return upper_bound(a,mid,r,val);
        }
    }
    public static int lower_bound(int[] a,int val){
        return lower_bound(a,0,a.length,val);
    }
    public static int lower_bound(int[] a,int l,int r,int val){
        if(r-l==1){
            if(a[l]<val) return r;
            return l;
        }
        int mid=(l+r)/2;
        if(a[mid]<val){
            return lower_bound(a,mid,r,val);
        }else{
            return lower_bound(a,l,mid,val);
        }

    }


    public static int max(int a,int b){
        return Math.max(a,b);
    }
    public static long max(long a,long b){
        return Math.max(a,b);
    }
    public static int abs(int a){
        return Math.abs(a);
    }
    public static long abs(long a){
        return Math.abs(a);
    }
    public static void print(Object object){
        System.out.print(object);
    }
    public static void put(Object object) {
        System.out.println(object);
    }
    public static void put(){
        System.out.println();
    }
    public static String format(String string, Object... args) {
        return String.format(string, args);
    }
}

final class Scanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }

    private boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
        return hasNextByte();
    }

    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }
}