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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.List;
import java.util.Queue;
import java.util.StringTokenizer;

public class Main {

    private static FastScanner scanner = new FastScanner(System.in);

    public static void main(String[] args) {
        int n = scanner.nextInt();
        long w = scanner.nextLong();

        int[] wArray = new int[n+1];
        int[] vArray = new int[n+1];
        for (int i = 1; i <= n; i++) {
            wArray[i] = scanner.nextInt();
            vArray[i] = scanner.nextInt();
        }

        // minWeight[i][j] -> i番目までの品物から価値がjになるように品物を選択したときの重さの総和の最小値
        // 初期値はすべての重さが最大値だった場合の総和より大きな値
        long[][] minWeight = new long[n+1][1000*n+1];
        for (int i = 0; i <= n; i++) {
            for (int j = 1; j <= 1000*n; j++) { // j=0の場合は、価値が0以上になる最小の重さになるので１つも選択しない場合の重さ0になる
                minWeight[i][j] = 1000000000L * 100L + 1L;
            }
        }

        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= 1000*n; j++) {
                minWeight[i][j] = minWeight[i-1][j];
                if (j - vArray[i] >= 0) {
                    minWeight[i][j] = Math.min(minWeight[i][j], minWeight[i-1][j-vArray[i]] + wArray[i]);
                }
            }
        }

        int maxValue = 0;
        for (int j = 1; j <= 1000*n; j++) {
            if (minWeight[n][j] <= w) {
                maxValue = j;
            }
        }
        System.out.println(maxValue);

    }


    // 最大公約数（大小の指定は問わない）
    private static int gcd(int s, int t) {
        int high = Math.max(s, t);
        int low = Math.min(s, t);

        int r = high % low;
        if (r == 0) return low;
        return gcd(low, r);
    }

    // 最小公倍数（大小の指定は問わない）
    private int lcm(int s, int t) {
        return s * t / gcd(s, t);
    }

    // グリッドグラフ
    private static class GridGraph {
        private int rLength;
        private int cLength;
        private String[][] gridGraph;
        private int[][] distance;

        public GridGraph(int r, int c) {
            this.rLength = r;
            this.cLength = c;
            this.gridGraph = new String[r][c];
            this.distance = new int[r][c];

            for (int i = 0; i < r; i++) {
                for (int j = 0; j < c; j++) {
                    this.distance[i][j] = -1;
                }
            }
        }

        public void setNode(int r, int c, String s) {
            this.gridGraph[r][c] = s;
        }

        // 幅優先探索
        public void bfs(int r, int c) {
            Queue<Coordinate> queue = new ArrayDeque<>();
            int[] dc = {1, 0, -1, 0};
            int[] dr = {0, 1, 0, -1};

            // スタート座標を探索キューに入れる
            queue.add(new Coordinate(r, c));
            // スタート座標の距離は0
            this.distance[r][c] = 0;

            while(!queue.isEmpty()) {
                Coordinate coo = queue.poll();

                for (int i = 0; i < 4; i++) {
                    int nc = coo.c + dc[i];
                    int nr = coo.r + dr[i];

                    // 範囲外座標はスルー
                    if (nc < 0 || nc >= this.cLength || nr < 0 || nr >= this.rLength) continue;
                    // 壁座標はスルー
                    if (this.gridGraph[nr][nc].equals("#")) continue;
                    // 到達済み座標はスルー
                    if (this.distance[nr][nc] >=0) continue;
                    // それ以外の座標は到達可能点として距離を記録して探索キューに入れる
                    this.distance[nr][nc] = this.distance[coo.r][coo.c] + 1;
                    queue.add(new Coordinate(nr, nc));
                }
            }
        }

        // 幅優先探索実施後にスタート座標からの距離を返す
        private int getDistance(int r, int c) {
            return this.distance[r][c];
        }

        // 座標
        private class Coordinate {
            int r;
            int c;
            public Coordinate(int r, int c) {
                this.r = r;
                this.c = c;
            }
        }
    }

    // グラフ
    private static class Graph {
        private Vertex[] vertexes;
        private int size;
        private boolean[] seen;

        public Graph(int n) {
            this.size = n;
            this.vertexes = new Vertex[n];
            for (int i = 0; i < n; i++) {
                this.vertexes[i] = new Vertex();
            }
            this.seen = new boolean[n];
        }

        public Graph(int[] vertexes) {
            this.size = vertexes.length;
            this. vertexes = new Vertex[vertexes.length];
            for (int i = 0; i < vertexes.length; i++) {
                this.vertexes[i] = new Vertex(vertexes[i]);
            }
            this.seen = new boolean[vertexes.length];
        }

        public void addEdge(int from, int to) {
            this.addEdge(from, to, 0);
        }

        public void addEdge(int from, int to, int weight) {
            this.vertexes[from].addEdge(to, weight);
        }

        // 深さ優先探索を実施し、到達可能な頂点をすべて辿り閉路かどうかをチェックする
        public boolean dfs(int now, int from) {
            this.seen[now] = true;
            boolean isCycle = false;
            for (Edge e : this.vertexes[now].getEdges()) {
                if (e.getTo() == from) {
                    continue;
                }
                if (seen[e.getTo()]) {
                    isCycle = true;
                } else {
                    isCycle = isCycle || dfs(e.getTo(), now);
                }
            }
            return isCycle;
        }

        // 深さ優先探索実施後に到達済みノードかどうかを返す
        public boolean seen(int now) {
            return this.seen[now];
        }

    }

    private static class Vertex {
        private int value;
        private List<Edge> edges = new ArrayList<>();

        public Vertex() {};
        public Vertex(int value) {
            this.value = value;
        }

        public void setValue(int value) {
            this.value = value;
        }

        public void addEdge(int to, int weight) {
            edges.add(new Edge(to, weight));
        }

        public List<Edge> getEdges() {
            return this.edges;
        }
    }

    private static class Edge {
        private int to;
        private int weight;

        public Edge(int to, int weight) {
            this.to = to;
            this.weight = weight;
        }

        public int getTo() {
            return this.to;
        }

        public int getWeight() {
            return this.weight;
        }
    }

    private static class FastScanner {

        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public FastScanner(InputStream in) {
            this.reader = new BufferedReader(new InputStreamReader(in));
        }

        public int[] nextLineToIntArray() {
            String[] stringArray = nextLineToStringArray();
            int[] intArray = new int[stringArray.length];
            for (int i = 0; i < stringArray.length; i++) {
                intArray[i] = Integer.parseInt(stringArray[i]);
            }
            return intArray;
        }

        public String[] nextLineToStringArray() {
            return nextLine().split("");
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
                throw new RuntimeException(e);
            }
        }

        public String next() {
            if (this.tokenizer == null || !this.tokenizer.hasMoreElements()) {
                try {
                    this.tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                    throw new RuntimeException(e);
                }
            }
            return this.tokenizer.nextToken();
        }

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

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

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

        public String[] nextStringArray(int n) {
            String[] stringArray = new String[n];
            for (int i = 0; i < n; i++) {
                stringArray[i] = next();
            }
            return stringArray;
        }

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

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

        public double[] nextDoubleArray(int n) {
            double[] doubleArray = new double[n];
            for (int i = 0; i < n; i++) {
                doubleArray[i] = nextDouble();
            }
            return doubleArray;
        }
    }
}