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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.TreeMap;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;
import java.util.SortedMap;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author vdewansa
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        EKnapsack2 solver = new EKnapsack2();
        solver.solve(1, in, out);
        out.close();
    }

    static class EKnapsack2 {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int N = in.nextInt();
            int W = in.nextInt();
            int[] w = new int[N + 1];
            int[] v = new int[N + 1];
            for (int i = 1; i <= N; i++) {
                w[i] = in.nextInt();
                v[i] = in.nextInt();
            }

            EKnapsack2.Monotonic prev = new EKnapsack2.Monotonic(W);
            EKnapsack2.Monotonic next = new EKnapsack2.Monotonic(W);
            for (int i = 1; i <= N; i++) {
                for (long wPrev : prev.keys()) {
                    long vPrev = prev.get(wPrev);
                    next.update(wPrev, vPrev);
                    next.update(wPrev + w[i], vPrev + v[i]);
                }
                next.update(w[i], v[i]);
                prev = next;
                next = new EKnapsack2.Monotonic(W);
            }
            out.println(prev.get(W));
        }

        static class Monotonic {
            private final long kMin = 0;
            private final long kMax;
            private final long vMin = 0;
            private SortedMap<Long, Long> m = new TreeMap<>();

            public Monotonic(long kMax) {
                this.kMax = kMax;
            }

            public long get(long k) {
                if (m.containsKey(k)) {
                    return m.get(k);
                }
                SortedMap<Long, Long> head = m.headMap(k);
                if (head.isEmpty()) {
                    return vMin;
                }
                return head.lastKey();
            }

            public void update(long k, long v) {
                if (k < kMin || k > kMax) {
                    return;
                }
                long oldV = get(k);
                if (v > oldV) {
                    m.put(k, v);
                }
                for (long tailK : m.tailMap(k).keySet()) {
                    if (v > m.get(tailK)) {
                        m.put(tailK, v);
                    }
                }
            }

            public Set<Long> keys() {
                return m.keySet();
            }

        }

    }
}