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: Accepted)

import java.io.*;
import java.lang.reflect.Array;
import java.util.Arrays;
import java.util.Stack;
import java.util.StringTokenizer;
public class Main{
    static int n;
    static int val[];
    static int weights[];
    static long memo[][];
    public static void main(String[] args) throws IOException {
        scanner sc = new scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        n = sc.nextInt();
        int w = sc.nextInt();
        val = new int[n];
        weights = new int[n];
        int sum = 0;
        for (int i = 0; i < n; i++) {
            weights[i] = sc.nextInt();
            val[i] = sc.nextInt();
            sum+= val[i];
        }

        memo = new long[n][sum+1];

        for (int i = 0; i < n; i++)
            Arrays.fill(memo[i],-1);

        int max = 0;

        for (int i = 1; i <= sum; i++) {
            if (dp(0,i) <= w)
                max = i;
        }

        out.println(max);
        out.flush();

    }

    static long dp(int i,int v){

        if (v == 0)
            return 0;

        if (i == n)
            return  (long) (1e9 +10);

        if (memo[i][v] != -1)
            return  memo[i][v];
        long take = (long) (1e9 +10);
        if (v-val[i] >= 0)
            take = dp(i+1,v-val[i]) + weights[i];

        long leave = dp(i+1,v);

        return memo[i][v] = Math.min(take,leave);
    }

}
class scanner{
    StringTokenizer st;
    BufferedReader br;
    public scanner(InputStream s){
        br = new BufferedReader(new InputStreamReader(s));
    }
    public scanner (String s) throws FileNotFoundException { br = new BufferedReader(new FileReader(s));}

    public String next() throws IOException {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

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

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

    public String nextLine() throws IOException {
        return br.readLine();
    }

    public boolean ready() throws IOException {
        return br.ready();
    }
}