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)

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

public class Main {

    static InputReader sc = new InputReader(System.in);
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) throws IOException {
        solver s = new solver();
        int t = 1;
        while (t > 0) {
            s.solve();
            t--;
        }
        out.close();
    }

    static class InputReader {

        public BufferedReader br;
        public StringTokenizer token;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream), 32768);
            token = null;
        }

        public String sn() {
            while (token == null || !token.hasMoreTokens()) {
                try {
                    token = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return token.nextToken();
        }

        public int ni() {
            return Integer.parseInt(sn());
        }

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

        public long nlo() {
            return Long.parseLong(sn());
        }

        public double nd() {
            return Double.parseDouble(sn());
        }

        public int[] na(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = sc.ni();
            return a;
        }

        public long[] nal(int n) {
            long a[] = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = sc.nlo();
            return a;
        }
    }

    static int inf = 5000013;

    static class solver {
        DecimalFormat df = new DecimalFormat("0.00000000");
        long maxi = 200000005;
        int n, val[];
        long w;
        long a[];

        void solve() {
            n = sc.ni();
            w = sc.nlo();
            int sum = 0;
            a=new long[n];
            val=new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = sc.nlo();
                val[i] = sc.ni();
                sum += val[i];
            }
            boolean sos[][] = new boolean[n + 1][sum + 1];
            for (int i = 0; i < n + 1; i++)
                sos[i][0] = true;
            for (int i = 1; i <= n; i++) {
                for (int j = 1; j <= sum; j++) {
                    if (j >= val[i - 1])
                        sos[i][j] = sos[i - 1][j] | sos[i - 1][j - val[i - 1]];
                    else
                        sos[i][j] = sos[i - 1][j];
                }
            }
            long dp[][] = new long[n + 1][sum + 1];
            for (int i = 1; i <= sum; i++)
                dp[0][i] = maxi;
            for (int i = 1; i <= n; i++) {
                for (int j = 1; j <= sum; j++) {
                    if (j >= val[i - 1])
                        dp[i][j] = Math.min(dp[i - 1][j], dp[i - 1][j - val[i - 1]] + a[i - 1]);
                    else
                        dp[i][j] = dp[i - 1][j];
                }
            }
            for (int i = sum; i >= 1; i--) {
                if (sos[n][i] && dp[n][i] <= w) {
                    out.println(i);
                    break;
                }
            }
        }
    }
}