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.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.OptionalInt;
import java.util.Scanner;
import java.io.PrintWriter;
import java.util.Scanner;
import java.util.stream.IntStream;
import java.util.stream.LongStream;

/**
 * E - Knapsack 2 / atcoder.jp
 * 문제 링크 : https://atcoder.jp/contests/dp/tasks/dp_e
 * 문제 해설 : https://jinpyo.kim/EducationalDP-solution
 * Submission : https://atcoder.jp/contests/dp/submissions/10058838
 */
public class Main {
    public static long Knapsack2(int N, int W, int[] ws, int[] vs) {
        // Java 8에서 새로 추가된 Stream을 사용해서, 합을 구해봅니다.
        int V = IntStream.of(vs).sum();
        OptionalInt W_MAX = IntStream.of(ws).max();

        // 문제의 'Constraints'에서 주어진것 처럼 Wi의 값이 매우 크기 때문에,
        // int를 사용해서 풀면, overflow 되는 문제가 발생합니다.
        long[][] dp = new long[N+1][V+1];

        for(int n=0; n<=N; ++n) {
            for(int v=0; v<=V; ++v) {
                // dp를 추후에 계산할 때, overflow가 되어서, - 값으로 바뀌는 것을 피하기 위해서
                // 모든 value의 합인 W_SUM 를 빼주게 됩니다.
                dp[n][v] = Long.MAX_VALUE - W_MAX.getAsInt();
            }
        }

        long value = 0;
        dp[0][0] = 0;
        for(int i=1; i<=N; ++i) {
            for(int v=0; v<=V; ++v) {
                dp[i][v] = Math.min(dp[i-1][v], dp[i][v]);
                if(v-vs[i]>=0)
                    dp[i][v] = Math.min(dp[i][v], dp[i-1][v-vs[i]] + ws[i]);
                if(dp[i][v] <= W) {
                    value = Math.max(value, v);
                }
            }
        }

        return value;
    }

    public static void main(String[] args) throws IOException {
//         Scanner sc = new Scanner(System.in);
        Reader sc = new Reader();
        int N = sc.nextInt();
        int W = sc.nextInt();
        int[] ws = new int[N+1];
        int[] vs = new int[N+1];
        PrintWriter pw = new PrintWriter(System.out);

        for(int i=1; i<=N; ++i) {
            ws[i] = sc.nextInt();
            vs[i] = sc.nextInt();
        }

        long r = Knapsack2(N, W, ws, vs);

        pw.println(r);
        pw.close();
    }

    // https://www.geeksforgeeks.org/fast-io-in-java-in-competitive-programming/
    static class Reader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }


}