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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;
import java.util.stream.IntStream;
import java.util.stream.Stream;

public class Main {

    public static void main(String[] args) throws IOException {
        new Main().solve();
    }

    private void solve() throws IOException {
        try {
//            solveA();
//            solveB();
//            solveC();
//            solveD();
//            solveE();
//            solveF();
            solveP1();
        } finally {
            if (in != null) {
                in.close();
            }
            if (out != null) {
                out.flush();
                out.close();
            }
        }

    }

    // mods
    long MOD = (long) Math.pow(10, 9) + 7;

    private void solveA() {
        int a = nextInt();
        int b = nextInt();
        for (int i = 1; i <= 3; i++) {
            if (i != a && i != b) {
                out.println(i);
                return;
            }
        }
    }

    private void solveB() {
        long n = nextLong();
        long k = nextLong();
        long res = k * (long) Math.pow(k - 1, n - 1);
        out.println(res);
    }

    private void solveC() {
        int n = nextInt();
        int[] a = new int[n + 2];
        long sum = 0;
        for (int i = 0; i < n + 2; i++) {
            if (i != 0 && i != n + 1)
                a[i] = nextInt();

            if (i != 0)
                sum += abs(a[i - 1] - a[i]);
        }
        for (int i = 1; i < n + 1; i++) {
            long oldP = abs(a[i - 1] - a[i]) + abs(a[i] - a[i + 1]);
            long newP = abs(a[i - 1] - a[i + 1]);
            out.println(sum - oldP + newP);
        }
    }

    private void solveD() {
        int h = nextInt();
        int w = nextInt();
        char[][] a = Stream.generate(() -> next().toCharArray()).limit(h).toArray(char[][]::new);
        Queue<SimplePair> queue = new ArrayDeque<SimplePair>();
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                if (a[i][j] == '#')
                    queue.add(new SimplePair(i, j));
            }
        }
        int[][] cnt = new int[h][w];
        for (int i = 0; i < h; i++) {
            Arrays.fill(cnt[i], -1);
        }
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                if (a[i][j] == '#') {
                    queue.add(new SimplePair(i, j));
                    cnt[i][j] = 0;
                }
            }
        }
        while (!queue.isEmpty()) {
            int max = queue.size();
            for (int i = 0; i < max; i++) {
                int[] dx = new int[]{-1, 0, 1, 0};
                int[] dy = new int[]{0, 1, 0, -1};
                SimplePair p = queue.poll();
                for (int j = 0; j < 4; j++) {
                    int wkX = (int) (p.k + dx[j]);
                    int wkY = (int) (p.v + dy[j]);
                    if (wkX < 0 || wkX >= h || wkY < 0 || wkY >= w || cnt[wkX][wkY] != -1)
                        continue;
                    cnt[wkX][wkY] = cnt[(int) p.k][(int) p.v] + 1;
                    queue.add(new SimplePair(wkX, wkY));
                }
            }
        }
        OptionalInt res = Arrays.stream(cnt).mapToInt(i -> Arrays.stream(i).max().getAsInt()).max();
        out.println(res.getAsInt());
    }

    private void solveE() {
        int n = nextInt();
        int[] a = IntStream.range(0, n).map(i -> nextInt()).toArray();
    }

    private void solveF() {

    }

    /**
     * EDPC E
     */
    private void solveP1() {
        int n = nextInt();
        int w = nextInt();
        int[][] wv = IntStream.range(0, n).mapToObj(i -> new int[]{nextInt(), nextInt()}).toArray(int[][]::new);
        int CONST = (int) (Math.pow(10, 5) + 1);
        long[][] dp = new long[n + 1][CONST];
        Arrays.fill(dp[0], 100_000_000_000L);
        dp[0][0] = 0;
        for (int i = 1; i <= n; i++) {
            for (int j = 0; j < CONST; j++) {
                int weight = wv[i - 1][0];
                int value = wv[i - 1][1];
                dp[i][j] = dp[i - 1][j];
                if (j - value >= 0)
                    dp[i][j] = Math.min(dp[i][j], dp[i - 1][j - value] + weight);
            }
        }
        for (int i = CONST - 1; i >= 0; i--) {
            if (dp[n][i] <= w) {
                out.println(i);
                return;
            }
        }

    }

    static final long CONST_INF = Long.MAX_VALUE / 4;

    public long[][] warshallFloyd(int n, int[][] edges) {
        long[][] graph = new long[n][n];
        for (int i = 0; i < n; i++) {
            Arrays.fill(graph[i], CONST_INF);
            graph[i][i] = 0;
        }
        int m = edges.length;
        for (int i = 0; i < m; i++) {
            int f = edges[i][0] - 1;
            int t = edges[i][1] - 1;
            long cost = edges[i][2];
            graph[f][t] = cost;
            graph[t][f] = cost;
        }
        for (int k = 0; k < n; k++) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    graph[i][j] = Math.min(graph[i][j], graph[i][k] + graph[k][j]);
                }
            }
        }
        return graph;
    }

    private static class VectorCalculation {
        /**
         * 点Pと線(AB)の距離
         *
         * @param p
         * @param a
         * @param b
         * @return
         */
        private double distanceDotAndLine(DoublePair p, DoublePair a, DoublePair b) {
            DoublePair ab = new DoublePair(b.x - a.x, b.y - a.y);
            DoublePair ap = new DoublePair(p.x - a.x, p.y - a.y);

            // ベクトルAB、APの外積の絶対値が平行四辺形Dの面積になる
            double d = Math.abs(crossVector(ab, ap));

            double l = distanceVertex(a, b); // AB間の距離

            double h = d / l;
            return h;
        }

        /**
         * 2点間距離
         *
         * @param p1
         * @param p2
         * @return
         */
        private double distanceVertex(DoublePair p1, DoublePair p2) {
            double dx = p1.x - p2.x;
            double dy = p1.y - p2.y;
            return Math.sqrt(dx * dx + dy * dy);
        }

        /**
         * ベクトル外積
         *
         * @param vl
         * @param vr
         * @return
         */
        private double crossVector(DoublePair vl, DoublePair vr) {
            return vl.x * vr.y - vl.y * vr.x;
        }
    }

    private static class DoublePair implements Comparable<DoublePair> {
        double x;
        double y;

        public DoublePair(double k, double v) {
            this.x = k;
            this.y = v;
        }

        public int compareTo(DoublePair pair) {
            return Double.compare(this.y, pair.y);
        }
    }

    private static class SimplePair implements Comparable<SimplePair> {
        long k;
        long v;

        public SimplePair(int k, int v) {
            this.k = k;
            this.v = v;
        }

        public SimplePair(long k, long v) {
            this.k = k;
            this.v = v;
        }

        public int compareTo(SimplePair pair) {
            return Long.compare(this.v, pair.v);
        }
    }


    private static class GraphNode {
        private long n;
        private Map<Long, SimplePair> childs;

        public GraphNode(long n) {
            this.n = n;
            childs = new TreeMap<Long, SimplePair>();
        }

        /**
         * not update
         *
         * @param child
         * @param d
         */
        public void addChild(long child, long d) {
            this.childs.put(child, this.childs.getOrDefault(child, new SimplePair(child, d)));
        }

        public SimplePair getChild(long child) {
            return this.childs.getOrDefault(child, new SimplePair(child, CONST_INF));
        }
    }

    private static class Graph {

        private Map<Long, GraphNode> graph;
        int n;

        /**
         * @param n    頂点数
         * @param list
         */
        public Graph(int n, int[][] list) {
            this.n = n;
            graph = new HashMap<Long, GraphNode>();
            /*
            隣接行列作成
            0-indexed
             */
            Arrays.stream(list).forEach(l -> {
                long a = l[0] - 1;
                long b = l[1] - 1;
                long d = l[2];
                graph.put(a, graph.getOrDefault(a, new GraphNode(a)));
                graph.get(a).addChild(b, d);
                graph.put(b, graph.getOrDefault(b, new GraphNode(b)));
                graph.get(b).addChild(a, d);
            });
            /*
            たどり着けない場所はCONST_INFで埋める
            自分へはCOST=0でたどり着ける
             */
            for (long i = 0; i < n; i++) {
                graph.put(i, graph.getOrDefault(i, new GraphNode(i)));
                GraphNode node = graph.get(i);
                for (int j = 0; j < n; j++) {
                    if (i == j)
                        node.addChild(j, 0L);
                    else
                        node.addChild(j, CONST_INF);
                }
            }
        }

        /**
         * ワーシャルフロイド
         */
        public void warshallFloyd() {
            for (long k = 0; k < n; k++) {
                for (long i = 0; i < n; i++) {
                    for (long j = 0; j < n; j++) {
                        long min = Math.min(graph.get(i).getChild(j).v, graph.get(i).getChild(k).v + graph.get(k).getChild(j).v);
                        graph.get(i).getChild(j).v = min;
                    }
                }
            }
        }

        /**
         * 2点間の距離
         *
         * @param from
         * @param to
         * @return
         */
        public long getDistance(long from, long to) {
            return graph.get(from).getChild(to).v;
        }

    }

    private static class SegTree {
        long e = 0;

        long calcFunc(long a, long b) {
            return a + b;
        }

        int n;
        long nodes[];

        public SegTree(long[] a) {
            init(a);
        }

        public SegTree(int len, long x) {
            long a[] = new long[len];
            Arrays.fill(a, x);
            init(a);
        }

        public SegTree(int len) {
            init(len);
        }

        void init(long[] a) {
            init(a.length);
            for (int i = 0; i < a.length; i++) {
                nodes[i + n - 1] = a[i];
            }
            for (int i = n - 2; i >= 0; i--) {
                nodes[i] = calcFunc(nodes[i * 2 + 1], nodes[i * 2 + 2]);
            }
        }

        void init(int len) {
            n = 1;
            while (n < len) {
                n *= 2;
            }
            nodes = new long[n * 2 - 1];
            Arrays.fill(nodes, e);
            for (int i = n - 2; i >= 0; i--) {
                nodes[i] = calcFunc(nodes[i * 2 + 1], nodes[i * 2 + 2]);
            }
        }

        void set(final int i, long val) {
            int wkI = i + n - 1;
            nodes[wkI] = val;
            while (wkI > 0) {
                wkI = (wkI - 1) / 2;
                nodes[wkI] = calcFunc(nodes[wkI * 2 + 1], nodes[wkI * 2 + 2]);
            }
        }

        long get(int i) {
            return find(i, i + 1);
        }

        /*
       要求区間 [a, b) 中の要素の最小値を答える
       k := 自分がいるノードのインデックス
       対象区間は [l, r) にあたる
        */
        long find(int a, int b) {
            return find(a, b, 0, 0, n);
        }

        long find(int a, int b, int k, int l, int r) {
            if (r < 0)
                r = n;

            if (b <= l || r <= a)
                return e;

            if (a <= l && r <= b)
                return nodes[k];

            long val1 = find(a, b, k * 2 + 1, l, (l + r) / 2);
            long val2 = find(a, b, k * 2 + 2, (l + r) / 2, r);
            //Math.min()
            //今回は区間内の個数なのでSUM
            return val1 + val2;
        }
    }

    private static class UnionFind {
        int[] pars;

        public UnionFind(int n) {
            pars = new int[n + 1];
            Arrays.fill(pars, -1);
        }

        public int getChilds(int n) {
            int wk = getRoot(n);
            return pars[wk];
        }

        public int getRoot(int n) {
            if (pars[n] < 0)
                return n;
            return pars[n] = getRoot(pars[n]);
        }

        public boolean isSame(int a, int b) {
            return getRoot(a) == getRoot(b);
        }

        private int getSize(int a) {
            return -pars[getRoot(a)];
        }

        public void unite(int a, int b) {
            int wkA = getRoot(a);
            int wkB = getRoot(b);
            if (wkA == wkB)
                return;

            if (getSize(wkA) < getSize(wkB)) {
                int tmp = wkA;
                wkA = wkB;
                wkB = tmp;
            }
            pars[wkA] = pars[wkA] + pars[wkB];
            pars[wkB] = wkA;
        }
    }

    public long calcSimpleCombination(long n, long m, long CONST_MOD) {
        long mole = 1;
        for (long i = 1; i <= n + m; i++) {
            mole *= i;
            mole %= CONST_MOD;
        }
        long deno = 1;
        for (long i = 1; i <= n; i++) {
            deno *= i;
            deno %= CONST_MOD;
        }
        for (int i = 1; i <= m; i++) {
            deno *= i;
            deno %= CONST_MOD;
        }
        deno = modInverse(deno, CONST_MOD);
        return (mole * deno) % CONST_MOD;
    }

    long abs(double x) {
        return (long) Math.abs(x);
    }

    long round(double x) {
        return Math.round(x);
    }

    long floor(double x) {
        return (long) Math.floor(x);
    }

    long ceil(double x) {
        return (long) Math.ceil(x);
    }

    double sqrt(double x) {
        return Math.sqrt(x);
    }

    double pow(double x, double y) {
        return Math.pow(x, y);
    }

    long pow(long x, long y) {
        return (long) Math.pow(x, y);
    }

    int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }

    int upperToInt(char a) {
        return a - 'A';
    }

    int lowerToInt(char a) {
        return a - 'a';
    }

    int numToInt(char a) {
        return a - '0';
    }

    int charToInt(char a) {
        return a >= 'a' ? lowerToInt(a) : a >= 'A' ? upperToInt(a) : numToInt(a);
    }

    char intToUpper(int a) {
        return (char) (a + 'A');
    }

    char intToLower(int a) {
        return (char) (a + 'a');
    }

    char intToNum(int a) {
        return (char) (a + '0');
    }

    void reverse(String array[]) {
        String reversed[] = new String[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void reverse(int array[]) {
        int reversed[] = new int[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void reverse(long array[]) {
        long reversed[] = new long[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void reverse(double array[]) {
        double reversed[] = new double[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void reverse(boolean array[]) {
        boolean reversed[] = new boolean[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void fill(int array[], int x) {
        Arrays.fill(array, x);
    }

    void fill(long array[], long x) {
        Arrays.fill(array, x);
    }

    void fill(double array[], double x) {
        Arrays.fill(array, x);
    }

    void fill(boolean array[], boolean x) {
        Arrays.fill(array, x);
    }

    void fill(int array[][], int x) {
        for (int a[] : array) {
            fill(a, x);
        }
    }

    void fill(long array[][], long x) {
        for (long a[] : array) {
            fill(a, x);
        }
    }

    void fill(double array[][], double x) {
        for (double a[] : array) {
            fill(a, x);
        }
    }

    void fill(boolean array[][], boolean x) {
        for (boolean a[] : array) {
            fill(a, x);
        }
    }

    void fill(int array[][][], int x) {
        for (int a[][] : array) {
            fill(a, x);
        }
    }

    void fill(long array[][][], long x) {
        for (long a[][] : array) {
            fill(a, x);
        }
    }

    void fill(double array[][][], double x) {
        for (double a[][] : array) {
            fill(a, x);
        }
    }

    void fill(boolean array[][][], boolean x) {
        for (boolean a[][] : array) {
            fill(a, x);
        }
    }

    long INF = (long) 1e18 + 7;

    boolean isINF(long a) {
        return abs(a) > INF / 1000;
    }

    boolean isPlusINF(long a) {
        return a > 0 && isINF(a);
    }

    boolean isMinusINF(long a) {
        return isPlusINF(-a);
    }

    int I_INF = (int) 1e9 + 7;

    boolean isINF(int a) {
        return abs(a) > I_INF / 1000;
    }

    boolean isPlusINF(int a) {
        return a > 0 && isINF(a);
    }

    boolean isMinusINF(int a) {
        return isPlusINF(-a);
    }

    public long mod(long i) {
        return i % MOD + ((i % MOD) < 0 ? MOD : 0);
    }

    long powMod(long x, long y) {
        if (y == 0) {
            return 1;
        } else {
            long tmp = powMod(x, y / 2);
            return mod(mod(tmp * tmp) * (y % 2 == 0 ? 1 : x));
        }
    }

    long[] powsMod(long x, int max) {
        long pow[] = new long[max + 1];
        pow[0] = 1;
        for (int i = 0; i < max; i++) {
            pow[i + 1] = mod(pow[i] * x);
        }
        return pow;
    }

    long inv(long x) {
        return powMod(x, MOD - 2);
    }

    int MAX_FACT = 5_000_100;
    long fact[];
    long invFact[];

    /**
     * Combination簡易版
     * 5 C 2
     * 異なる n個のものから r個を選ぶ組み合わせの総数 nCr を求めます。
     * 5!(5*4*3*2*1)
     * /
     * 2!(2*1) *  (5-2)!(3*2*1)
     *
     * @param n
     * @param r
     * @return
     */
    private long getComb(int n, int r) {
        long tmp = 1;
        for (int i = 1; i <= r; i++) {
            tmp *= n - i + 1;
            tmp = mod(tmp);
            tmp *= inv(i);
            tmp = mod(tmp);
        }
        return tmp;
    }

    /**
     * 階乗計算の事前累積和
     * [1, 1, 2, 3, 4, 5, … FACTORIAL_NUM]
     * mod済
     */
    void prepareFact() {
        fact = new long[MAX_FACT];
        Arrays.fill(fact, 0);
        invFact = new long[MAX_FACT];
        Arrays.fill(invFact, 0);
        fact[0] = 1;
        int maxIndex = (int) min(MAX_FACT, (int) MOD);
        for (int i = 1; i < maxIndex; i++) {
            fact[i] = mod(fact[i - 1] * i);
        }
        invFact[maxIndex - 1] = inv(fact[maxIndex - 1]);
        for (int i = maxIndex - 1; i > 0; i--) {
            invFact[i - 1] = mod(invFact[i] * i);
        }
    }

    /**
     * 順列
     * nPk -> n! / (n-k)!
     *
     * @param n
     * @param r
     * @return
     */
    long permutation(int n, int r) {
        if (n < 0 || r < 0 || n < r) {
            return 0;
        }
        return mod(fact[n] * invFact[n - r]);
    }

    /**
     * 組み合わせ
     * nCk -> n! / k!・(n-k)!
     *
     * @param n
     * @param r
     * @return
     */
    long combination(int n, int r) {
        if (n < 0 || r < 0 || n < r) {
            return 0;
        }
        return mod(permutation(n, r) * invFact[r]);
    }

    /**
     * 重複組合せ nHr （同次積）
     * nHr = (n+r-1)Cr
     * 異なるn個のものから重複を許してr個取る組合せの総数
     * 例：
     * リンゴ，ミカン，牛肉の3種類の果物があります．これらの中から6個の食材を買って帰ります．
     * このとき，何通りの買い方がありますか？ただし，含まれない食材があってもよいものとします
     *
     * @param n
     * @param r
     * @return
     */
    long homogeneousProduct(int n, int r) {
        return combination((n - 1) + r, r);
    }

    /**
     * 多項係数
     * 文字aをp個,bをq個,cをr個, dをs個 あわせてn個を1列に並べるときの並べ方
     * n! / p!・q!・r!・s!
     *
     * @param n
     * @param strNum
     * @param mod
     * @return
     */

    /**
     * フェルマーの小定理を用いて逆元を求める。
     * ある数xのmod p（pは素数）の逆数x'はx' = x^(p-2)
     * 繰り返し二乗法を用いて計算する。
     * http://satanic0258.hatenablog.com/entry/2016/04/29/004730
     * {@link BigInteger#modInverse(BigInteger)}とどちらが速いか？
     *
     * @param x
     * @return
     */
    private long modInverse(long x, long mod) {
        long res = 1L;
        long k = mod - 2L;
        long y = x;
        while (k != 0) {
            if (k % 2 != 0) {
                res = (res * y) % mod;
            }
            y = (y * y) % mod;
            k /= 2;
        }
        return res;
    }


    private final PrintWriter out = new PrintWriter(System.out);
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }

    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
    }

    public boolean hasNext() {
        skipUnprintable();
        return hasNextByte();
    }

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

    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public long min(long... v) {
        long min = Long.MAX_VALUE;
        for (long i : v) min = Math.min(min, i);
        return min;
    }

    public long max(long... v) {
        long max = Long.MIN_VALUE;
        for (long i : v) max = Math.max(max, i);
        return max;
    }
}