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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

/*
    Arnab Chanda 
*/

// All imports here

import java.io.InputStreamReader;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.InputStream;
import java.util.*;
import java.util.stream.Collectors;

// Template code starts here //

//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Debugger debug = new Debugger(out);
        Objectify objectify = new Objectify(debug);
        Task solver = new Task();
        int test = 1;
        while(test-->0){
            solver.solve(1, in, out, debug, objectify);
        }
		out.close();
	}
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;
 
    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }
 
    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }
 
    public int nextInt() {
        return Integer.parseInt(next());
    }

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

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

    public float nextFloat() {
        return Float.parseFloat(next());
    }
 
}

class Debugger{
    PrintWriter out;

    Debugger(PrintWriter out){    
        this.out = out;
    }

    public <T> void printList(List<T> arrayList){
        for( Object ob: arrayList){
            out.print(ob+" ");
        }
        out.println();
    }

    public <T> void printSet(Set<T> set){
        for(Object ob: set){
            out.print(ob+" ");
        }
        out.println();
    }

    public <T> void printMap(Map<?,?> map){
        for(Object ob: map.keySet()){
            System.out.println(ob+" : "+map.get(ob));
        }
    }
}

class Objectify{
    
    Debugger debug;

    Objectify(Debugger ob){ debug = ob; }

    public void printArr(int[] arr){ debug.printList(Arrays.stream(arr).boxed().collect(Collectors.toList())); }
    public void printArr(double[] arr){ debug.printList(Arrays.stream(arr).boxed().collect(Collectors.toList())); }
    public void printArr(long[] arr){ debug.printList(Arrays.stream(arr).boxed().collect(Collectors.toList())); }
    public void printArr(char[] arr){ debug.printList( String.valueOf(arr).chars().mapToObj(c -> (char) c).collect(Collectors.toList())); }
    public void printArr(String[] arr){ debug.printList(Arrays.asList(arr)); }

    public void printMatrix(int[][] arr){ for(int a[]:arr) printArr(a); }
    public void printMatrix(double[][] arr){ for(double a[]:arr) printArr(a); }
    public void printMatrix(long[][] arr){ for(long a[]:arr) printArr(a); }
    public void printMatrix(char[][] arr){ for(char a[]:arr) printArr(a); }
    public void printMatrix(String[][] arr){ for(String a[]:arr) printArr(a); }

}

//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

// Template code ends here


class Task {

    final long MOD = (int)Math.pow(10,9)+7;

    final int V_SUM_MAX = 100000; 
    final int N_MAX = 100; 
    final int W_MAX = 1000000000; 
      
    // To store the states of DP  
    int dp[][] = new int[V_SUM_MAX + 1][N_MAX];  
    boolean v[][] = new boolean [V_SUM_MAX + 1][N_MAX];  
      
    // Function to solve the recurrence relation  
    public int solveDp(int r, int i, int w[],        
                          int val[], int n)  
    {  
        // Base cases  
        if (r <= 0)  
            return 0;  
              
        if (i == n)  
            return W_MAX;  
              
        if (v[r][i])  
            return dp[r][i];  
      
        // Marking state as solved  
        v[r][i] = true;  
      
        // Recurrence relation  
        dp[r][i] = Math.min(solveDp(r, i + 1, w, val, n),  
                     w[i] + solveDp(r - val[i],  
                                    i + 1, w, val, n));  
          
        return dp[r][i];  
    }  
      
    // Function to return the maximum weight  
    public int maxWeight(int w[], int val[],  
                         int n, int c)  
    {  
      
        // Iterating through all possible values  
        // to find the the largest value that can  
        // be represented by the given weights  
        for (int i = V_SUM_MAX; i >= 0; i--) 
        {  
            if (solveDp(i, 0, w, val, n) <= c)  
            {  
                return i;  
            }  
        }  
        return 0;  
    } 
    public void solve(int testNumber, InputReader sc, PrintWriter out, Debugger debug, Objectify objectify) {
        
        // write your code here
        int n = sc.nextInt();
        int w = sc.nextInt();

        int wt[] = new int[n];
        int val[] = new int[n];

        for(int  i = 0; i < n; i++){
            wt[i] = sc.nextInt();
            val[i] = sc.nextInt();
        }

        out.println(maxWeight(wt, val, n, w));

    }
}