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: Runtime Error)



import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.StringTokenizer;

public class Main {
    final static long MOD = 1000000007;

    public static void main(String args[]) {
        FastScanner fs = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);

        int n = fs.nextInt();
        int w = fs.nextInt();

        Pair [] items = new Pair[n];

        for(int i = 0; i < n; i++) {
            items[i] = new Pair(fs.nextInt(), fs.nextInt());
        }

        Arrays.sort(items, (o1, o2) -> Integer.compare(o1.w, o2.w));

        short dp[][] = new short[3][w+1];

        for(int i = 0; i < 3; i++) {
            for(int j = 0; j < w+1; j++) {
                if(i == 0 || j ==0) {
                    dp[i][j] = 0;
                }
            }
        }
        int currentRow = 1;
        for(int i = 1; i < n+1; i++) {
            for(int j = 1; j < w+1; j++) {
               {
                    if(j - items[i-1].w >= 0) {
                        dp[currentRow][j] = (short) Math.max(dp[currentRow - 1][j - items[i-1].w] + items[i-1].v, dp[currentRow - 1][j]);
                    } else {
                        dp[currentRow][j] = dp[currentRow - 1][j];
                    }
                }
            }
            if(currentRow == 2)
                dp[1] = Arrays.copyOf(dp[2], dp[2].length);
            //Arrays.fill(dp[2], 0);
            //Arrays.fill(dp[2], 0);
            currentRow = 2;
        }
       /* for(int i = 1; i < 3; i++) {
            out.println(i+" "+ Arrays.toString(dp[i]));
        }*/
        out.println(dp[2][w]);
        out.flush();
        out.close();
    }

    static class Pair {
        int w;
        int v;

        Pair(int w, int v) {
            this.v = v;
            this.w = w;
        }

        @Override
        public String toString() {
            return "("+this.w+", "+this.v+")";
        }
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            try {
                br = new BufferedReader(new InputStreamReader(System.in));
                //                br = new BufferedReader(new FileReader("file2.txt"));

                st = new StringTokenizer("");
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        public String next() {
            if (st.hasMoreTokens())
                return st.nextToken();
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                e.printStackTrace();
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            String line = "";
            try {
                line = br.readLine();
            } catch (Exception e) {
                e.printStackTrace();
            }
            return line;
        }

        public char nextChar() {
            return next().charAt(0);
        }

        public Integer[] nextIntegerArray(int n) {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }

        public char[] nextCharArray() {
            return nextLine().toCharArray();
        }
    }

}