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)

import java.util.*;
import java.io.*;

class Main {

    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

    static final Reader in = new Reader();
    static int N, W; // ..maximum capacity of knapsack
    static int[] w; // ..weight array
    static int[] v; // .. value or price array
    static HashSet<Integer> items_set = new HashSet<>();

    static long[][] dp;

    public static void main(String[] args) throws Exception {
        N = in.nextInt();
        W = in.nextInt();
        w = new int[N + 1];
        v = new int[N + 1];

        dp = new long[N + 1][W + 1];

        for (int i = 1; i <= N; i++) {
            w[i] = in.nextInt();
            v[i] = in.nextInt();
            items_set.add(i);
            Arrays.fill(dp[i], -1); 
        }

        System.out.println(knapSack(W, N));
    }

    static long knapSack(int c, int i) {
        // base condition
        if (i < 0)
            return 0;

        //..if value already exists directly return    
        if (dp[i][c] != -1)
            return dp[i][c];

        if (w[i] <= c) {
            //..ignore ith element and consider rest of i-1 elements
            long temp1 = knapSack(c, i - 1);
            //..consider ith element so reduce capacity
            long temp2 = v[i] + knapSack(c - w[i], i - 1);

            //..store it
            dp[i][c] = Math.max(temp1,temp2);

            return dp[i][c];

        } else { // ..weight of ith element is more than c
            dp[i][c] = knapSack(c, i - 1);
            return dp[i][c];
        }
    }

    static long k(int W, int i) {
        // base condition
        if (i < 0)
            return 0;
            
        if (dp[i][W] != -1)
            return dp[i][W];
 
        if (w[i] <= W) {
            dp[i][W] = Math.max(v[i] + knapSack(W - w[i],i - 1), knapSack(W,i - 1));
            return dp[i][W];
            
        } else {
            dp[i][W] = knapSack(W,i - 1);
            return dp[i][W];
        }
    }

    

}