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 10^9

1 \leq w_i \leq W

1 \leq v_i \leq 10^3

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

1 1000000000
1000000000 10

Sample Output 2

10

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: Time Limit Exceeded)

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


class Solver {            
    StringBuilder out=new StringBuilder(100);
    FastReader in=new FastReader();
    public long pow(long a, long b){
        if(b==0)return 1;
            long ans=pow(a,b/2);
            ans*=ans;
            ans%=mod;
        if(b%2==1){
            ans*=a;
            ans%=mod;
        }
        return ans;
    }
    
    public int[] getIntArray(int n){
        int arr[]=new int[n];
        for(int i=0;i<n;i++){
            arr[i]=in.nextInt();
        }
        return arr;
    }

    int  mod=(int)(1e9 + 7);
    HashMap<Integer, HashMap<Integer, Integer>>dp=new HashMap<>();
    int n,k;
    int v[], w[];
    public int recur(int i, Integer weight){
        if(i==n)return 0;
        if(dp.containsKey(i) && dp.get(i).containsKey(weight)){
            return dp.get(i).get(weight);
        }
        int inc=0, ninc=recur(i+1, weight);
        if(weight-w[i]>=0){
            inc=v[i]+recur(i+1,weight-w[i]);
        }
        int ans=Math.max(inc, ninc);
        if(!dp.containsKey(inc))dp.put(i, new HashMap<>());
        dp.get(i).put(weight,ans);
        return ans;
    }
    public void solve(){
        n=in.nextInt();k=in.nextInt();
        w=new int[n];
        v=new int[n];
        for(int i=0;i<n;i++){
            w[i]=in.nextInt();
            v[i]=in.nextInt();
        }
        out.append(recur(0,k));
    }
    public void run(){
        int t=1;
        for(int i=0;i<t;i++){
            solve();
            out.append('\n');
        }
        System.out.println(out);
    }
}
    
    
    
    
    
/////////////////////
    
    
    
    
    
    
    public class Main{
        public static void main(String args[]){
            Solver s=new Solver();
            s.run();
        }
    } 
    
    class FastReader { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
    
        public FastReader() { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
    
        public FastReader(String file_name) throws IOException{ 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
    
        public String nextLine() { 
            try{
                byte[] buf = new byte[10000000]; // line length 
                int cnt = 0, c; 
                while ((c = read()) != -1) { 
                    if (c == '\n') 
                        break; 
                    buf[cnt++] = (byte) c; 
                } 
                return new String(buf, 0, cnt); 
            }catch (Exception e){
                System.out.println(e.getMessage());
                return null;
            }
        } 
    
        public int nextInt()  { 
            int ret = 0; 
            try {
                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; 
            } catch (Exception e) {
                System.out.println(e.getMessage());
                return -1;
            }
        } 
    
        public long nextLong()   { 
            
            try {
                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;
            } catch (Exception e) {
                System.out.println(e.getMessage());
                return -1;
            }
        } 
    
        public double nextDouble()  { 
            
            try {
                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;
            } catch (Exception e) {
                System.out.println(e.getMessage());
                return -1;
            }
        } 
    
        private void fillBuffer() throws IOException{ 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
    
        private byte read() throws IOException  { 
            try{
                if (bufferPointer == bytesRead) 
                    fillBuffer(); 
                return buffer[bufferPointer++]; 
            }catch(Exception e){
                System.out.println(e.getMessage());
                return -1;
            }
        } 
    
        public void close() throws IOException { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 


    // 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;
    //     }
    // }