Problem:
Score : 100 points

Problem Statement

There are N items, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq N), Item i has a weight of w_i and a value of v_i.

Taro has decided to choose some of the N items and carry them home in a knapsack.
The capacity of the knapsack is W, which means that the sum of the weights of items taken must be at most W.

Find the maximum possible sum of the values of items that Taro takes home.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq W \leq 10^5

1 \leq w_i \leq W

1 \leq v_i \leq 10^9

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 sum of the values of items that Taro takes home.

Sample Input 1

3 8
3 30
4 50
5 60

Sample Output 1

90

Items 1 and 3 should be taken.
Then, the sum of the weights is 3 + 5 = 8, and the sum of the values is 30 + 60 = 90.

Sample Input 2

5 5
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000

Sample Output 2

5000000000

The answer may not fit into a 32-bit integer type.

Sample Input 3

6 15
6 5
5 6
6 4
6 6
3 5
7 2

Sample Output 3

17

Items 2, 4 and 5 should be taken.
Then, the sum of the weights is 5 + 6 + 3 = 14, and the sum of the values is 6 + 6 + 5 = 17.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)


//package cf;
import java.io.*;
import java.util.*;
public class Main {
    static int p=1000000007;
    public static void main(String[] args) throws Exception{
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(java.io.FileDescriptor.out), "ASCII"), 512);
        FastReader sc=new FastReader();
        int n = sc.nextInt();
        int W = sc.nextInt();
        int w[]=new int[n];
        int v[]=new int[n];
        for(int i=0;i<n;i++)
        {
            w[i]=sc.nextInt();
            v[i]=sc.nextInt();
        }

        StringBuilder sb=new StringBuilder();
        long dp[][]=new long[n+1][W+1];
        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=W;j++)
            {
                if(j-w[i-1]>=0)
                {
                    dp[i][j]=Math.max(dp[i-1][j],v[i-1]+dp[i-1][j-w[i-1]]);
                 //   System.out.println(i+"  "+j+" "+dp[i][j]);
                }
                else
                {
                    dp[i][j]=Math.max(dp[i][j],dp[i-1][j]);
                }
            }
        }
        sb.append(dp[n][W]);
        out.write(sb.toString());
        out.flush();
    }


static class pair
{
    long a,d;
    StringBuilder sb;

    public pair(long a, long d, StringBuilder sb) {
        this.a = a;
        this.d = d;
        this.sb = sb;
    }
}



    ///////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////
    static class FastReader {

        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }


}