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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var line = consoleReader.Split.Int;
            var N = line[0];
            var W = line[1];
            var g = consoleReader.Repeat(N).SplitInt.Select(Goods.Create).ToArray();

            var dic = new Dictionary<int, long>();
            dic[0] = 0;
            dic[g[0].weight] = g[0].value;
            for (int i = 1; i < N; i++)
            {
                var value = g[i].value;
                var weight = g[i].weight;
                var keys = dic.Keys.Reverse().ToArray();
                foreach (var key in keys)
                {
                    var nextKey = key + weight;
                    if (nextKey <= W)
                    {
                        long next;
                        dic.TryGetValue(nextKey, out next);
                        dic[nextKey] = Math.Max(next, dic[key] + value);
                    }
                }
            }

            return dic.Values.Max();
        }

        struct Goods
        {
            public static Goods Create(int[] l) => new Goods { weight = l[0], value = l[1] };
            public int weight;
            public int value;
        }

        #region いつもの
        private readonly ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader()).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
        #endregion
    }
    struct Mod : IEquatable<Mod>
    {
        public const long mod = 1000000007;
        public readonly long val;
        public Mod(long val) { this.val = val; }
        public override bool Equals(object obj) => (obj is Mod) ? this == ((Mod)obj) : false;
        public bool Equals(Mod obj) => this == obj;
        public override int GetHashCode() => val.GetHashCode();
        public override string ToString() => val.ToString();
        public static implicit operator Mod(long x) => new Mod(x);
        public static Mod operator +(Mod x, Mod y) => (x.val + y.val) % mod;
        public static Mod operator -(Mod x, Mod y) => x.val >= y.val ? (x.val - y.val) % mod : (x.val - y.val) % mod + mod;
        public static Mod operator *(Mod x, Mod y) => (x.val * y.val) % mod;
        public static Mod operator /(Mod x, Mod y) => x * y.Inverse();
        public static bool operator ==(Mod x, Mod y) => x.val == y.val;
        public static bool operator !=(Mod x, Mod y) => x.val != y.val;
        public Mod Inverse()
        {
            long a = val, b = mod, u = 1, v = 0;
            while (b > 0)
            {
                long t = a / b;
                var b2 = a - t * b;
                a = b; b = b2;
                var v2 = u - t * v;
                u = v; v = v2;
            }
            u %= mod;
            if (u < 0) u += mod;
            return u;
        }
        public static Mod Pow(Mod x, int y)
        {
            Mod res = 1;
            for (; y > 0; y >>= 1)
            {
                if ((y & 1) == 1) res *= x;
                x *= x;
            }
            return res;
        }

        public static Factor CreateFactor(int max) => new Factor(max);
        public class Factor
        {
            private readonly Mod[] fac, finv;
            public Factor(int max)
            {
                var inv = new Mod[max];
                fac = new Mod[max]; finv = new Mod[max];
                fac[0] = fac[1] = 1;
                finv[0] = finv[1] = 1;
                inv[1] = 1;
                for (int i = 2; i < max; i++)
                {
                    fac[i] = fac[i - 1] * i;
                    inv[i] = mod - inv[mod % i].val * (mod / i) % mod;
                    finv[i] = finv[i - 1] * inv[i];
                }
            }

            // 二項係数計算
            public Mod Combine(int n, int k)
            {
                if (n < k) return 0;
                if (n < 0 || k < 0) return 0;
                return fac[n] * finv[k] * finv[n - k];
            }

            public Mod Factorial(int n) => fac[n];
            public Mod FactorialInvers(int n) => finv[n];
        }
    }

#pragma warning disable
    public class ConsoleReader { public class SplitLine { string[] splited; public SplitLine(string line) { splited = line.Split(); } public string[] String => splited.ToArray(); public int[] Int => splited.Select(int.Parse).ToArray(); public long[] Long => splited.Select(long.Parse).ToArray(); public ulong[] ULong => splited.Select(ulong.Parse).ToArray(); public double[] Double => splited.Select(double.Parse).ToArray(); } public class RepeatLine { ConsoleReader reader; int num; public RepeatLine(ConsoleReader reader, int num) { this.reader = reader; this.num = num; } public IEnumerable<string> String { get { for (int i = 0; i < num; i++) yield return reader.String; } } public IEnumerable<int> Int { get { for (int i = 0; i < num; i++) yield return reader.Int; } } public IEnumerable<long> Long { get { for (int i = 0; i < num; i++) yield return reader.Long; } } public IEnumerable<string[]> Split { get { for (int i = 0; i < num; i++) yield return reader.Split.String; } } public IEnumerable<int[]> SplitInt { get { for (int i = 0; i < num; i++) yield return reader.Split.Int; } } } public virtual string String => Console.ReadLine(); public int Int => int.Parse(String); public long Long => long.Parse(String); public ulong ULong => ulong.Parse(String); public double Double => double.Parse(String); public SplitLine Split => new SplitLine(String); public RepeatLine Repeat(int count) => new RepeatLine(this, count); }
}