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: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using static Ha2ne2Util.Cin;
using static Ha2ne2Util.Util;
using static System.Console;
using static System.Math;
using System.Collections;

namespace ABC153
{
    class Program
    {

        static void Main(string[] args)
        {
        START:
            // A();  20m 20m
            // B();  27m  7m
            // C();  69m 42m
            // D(); 139m 70m
            // E(); 70m
            E2();
            // F();

#if DEBUG
            goto START;
#endif
        }

        private static void F()
        {

        }

        private static void E2()
        {
            long N = ReadLong();
            long W = ReadLong();
            long[] ws = new long[N];
            long[] vs = new long[N];
            for (int i = 0; i < N; i++)
            {
                ws[i] = ReadLong();
                vs[i] = ReadLong();
            }

            long maxValue = 100000;
            long[,] dp = new long[N + 1, maxValue + 1];

            for(int i = 0; i <= N; i++)
            {
                for(int j = 0; j <= maxValue; j++)
                {
                    dp[i, j] = Ha2ne2Util.Util.INF;
                }
            }

            dp[0, 0] = 0;
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j <= maxValue; j++)
                {
                    if (j - vs[i] >= 0)
                    {
                        dp[i + 1, j] = Min(
                            dp[i, j],
                            dp[i, j - vs[i]] + ws[i]
                            );
                    }
                    else
                    {
                        dp[i + 1, j] = dp[i, j];
                    }
                }
            }

            long ans = 0;
            for (int i = 0; i <= maxValue; i++)
            {
                if (dp[N, i] <= W)
                    ans = i;
            }

            WriteLine(ans);
        }

        static long INF = 1000000000000000;

        private static void E()
        {
            long N = ReadLong();
            long W = ReadLong();
            long[] ws = new long[N];
            long[] vs = new long[N];
            for (int i = 0; i < N; i++)
            {
                ws[i] = ReadLong();
                vs[i] = ReadLong();
            }

            int maxValue = 100000;
            long[,] dp = new long[N + 1, maxValue + 1];
            for (int i = 0; i < N; i++)
            {
                for (int v = 0; v <= maxValue; v++)
                {
                    dp[i, v] = INF;
                }
            }

            dp[0, 0] = 0;
            for (int i = 0; i < N; i++) 
            {
                for (int v = 0; v <= maxValue; v++)
                {
                    if (vs[i] <= v)
                    {
                        dp[i + 1, v] = Min(
                            dp[i, v],
                            dp[i, v - vs[i]] + ws[i]);
                    }
                    else
                    {
                        dp[i + 1, v] = dp[i, v];
                    }
                }
            }

            long ans = 0;
            for (int i = 0; i <= maxValue; i++)
            {
                if (dp[N, i] <= W)
                    ans = i;
            }

            WriteLine(ans);
        }

        class Jewel
        {
            public long w { get; set; }
            public long v { get; set; }
        }

        private static void D()
        {
            long N = ReadLong();
            long W = ReadLong();
            Jewel[] jewels = new Jewel[N];
            for (int i = 0; i < N; i++)
            {
                var j = new Jewel();
                j.w = ReadLong();
                j.v = ReadLong();
                jewels[i] = j;
            }

            long[,] dp = new long[N + 1, W + 1];

            for (int i = 0; i < N; i++)
            {
                for (int w = 0; w <= W; w++)
                {
                    if (w < jewels[i].w)
                    {
                        dp[i + 1, w] = dp[i, w];
                    }
                    else
                    {
                        dp[i+1, w] = Max(
                            dp[i, w],
                            dp[i, w - jewels[i].w] + jewels[i].v);
                    }
                }
            }

            WriteLine(dp[N,W]);
        }

        private static void C()
        {
            long N = ReadLong();
            long[] A = new long[N];
            long[] B = new long[N];
            long[] C = new long[N];

            for (int i = 0; i < N; i++)
            {
                A[i] = ReadLong();
                B[i] = ReadLong();
                C[i] = ReadLong();
            }

            long[,] dp = new long[N, 3];
            dp[0, 0] = A[0];
            dp[0, 1] = B[0];
            dp[0, 2] = C[0];

            for (int i = 0; i < N-1; i++)
            {
                int ni = i + 1;

                // Aからの遷移
                dp[ni, 1] = Max(dp[ni, 1], dp[i, 0] + B[ni]);
                dp[ni, 2] = Max(dp[ni, 2], dp[i, 0] + C[ni]);

                // Bからの遷移
                dp[ni, 0] = Max(dp[ni, 0], dp[i, 1] + A[ni]);
                dp[ni, 2] = Max(dp[ni, 2], dp[i, 1] + C[ni]);

                // Cからの遷移
                dp[ni, 0] = Max(dp[ni, 0], dp[i, 2] + A[ni]);
                dp[ni, 1] = Max(dp[ni, 1], dp[i, 2] + B[ni]);
            }

            long ans = Max(Max(dp[N - 1, 0], dp[N - 1, 1]), dp[N - 1, 2]);

            WriteLine(ans);
        }

       
        private static void B()
        {
            long N = ReadLong();
            long K = ReadLong();
            long[] H = ReadLongArray();

            long[] dp = new long[N];

            for (int i = 0; i < N; i++)
                dp[i] = long.MaxValue;

            dp[0] = 0;

            for (int i = 0; i < N; i++)
            {
                if (dp[i] == long.MaxValue) continue;
                for (int j = 1; j <= K; j++)
                {
                    if (i + j < N)
                        dp[i + j] = Min(dp[i + j], dp[i] + Abs(H[i] - H[i + j]));
                }
            }

            WriteLine(dp[N - 1]);
        }

        private static void A()
        {
            long N = ReadLong();
            long[] H = ReadLongArray();

            long[] dp = new long[N];

            for (int i = 0; i < N; i++)
                dp[i] = long.MaxValue;

            dp[0] = 0;

            for(int i = 0; i < N; i++)
            {
                if (dp[i] == long.MaxValue) continue;
                if (i + 1 < N)
                    dp[i + 1] = Min(dp[i + 1], dp[i] + Abs(H[i] - H[i + 1]));

                if (i + 2 < N)
                    dp[i + 2] = Min(dp[i + 2], dp[i] + Abs(H[i] - H[i + 2]));
            }

            WriteLine(dp[N-1]);
        }
    }
}

namespace Ha2ne2Util
{
    public static class Cin
    {
        static string[] Tokens { get; set; }

        static int Ptr { get; set; }

        public static string Next()
        {
            if (Tokens == null || Tokens.Length <= Ptr)
            {
                Tokens = Console.ReadLine().Split(' ');
                Ptr = 0;
            }

            return Tokens[Ptr++];
        }

        public static int ReadInt()
        {
            return int.Parse(Next());
        }

        public static long ReadLong()
        {
            return long.Parse(Next());
        }

        public static int[] ReadIntArray()
        {
            Tokens = null;
            return Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
        }

        public static long[] ReadLongArray()
        {
            Tokens = null;
            return Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
        }

        public static int[][] ReadIntTable(int n)
        {
            Tokens = null;
            int[][] ret = new int[n][];
            for (int i = 0; i < n; i++)
            {
                ret[i] = ReadIntArray();
            }

            return ret;
        }

        public static long[][] ReadLongTable(long n)
        {
            Tokens = null;
            long[][] ret = new long[n][];
            for (long i = 0; i < n; i++)
            {
                ret[i] = ReadLongArray();
            }

            return ret;
        }

        public static string ReadString()
        {
            return Next();
        }

        /// <summary>
        /// "00101001010"という様な入力をintの配列にして返す
        /// </summary>
        /// <returns></returns>
        public static int[] ReadIntArrayFromBinaryString()
        {
            Tokens = null;
            return Array.ConvertAll(Console.ReadLine().ToArray(), c => int.Parse(c.ToString()));
        }

        /// <summary>
        /// "00101001010"という様な入力をboolの配列にして返す
        /// </summary>
        /// <returns></returns>
        public static bool[] ReadBoolArrayFromBinaryString()
        {
            Tokens = null;
            return Console.ReadLine().Select(c => c == '1').ToArray();
        }
    }

    /// <summary>
    /// ユーティリティー
    /// </summary>
    public static class Util
    {
        // 10^17
        public static readonly long INF = (long)1e17;

        public static IEnumerable<int> Range(int end)
        {
            for (int i = 0; i < end; i++)
            {
                yield return i;
            }
        }

        public static IEnumerable<int> Range(int from, int end)
        {
            for (int i = from; i < end; i++)
            {
                yield return i;
            }
        }

        public static IEnumerable<int> Range(int from, int end, int step)
        {
            for (int i = from; i < end; i += step)
            {
                yield return i;
            }
        }

        /// <summary>
        /// ソートをして結果を返します。
        /// 破壊的関数です。
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="array"></param>
        /// <returns></returns>
        public static T[] Sort<T>(T[] array)
        {
            Array.Sort<T>(array);
            return array;
        }

        /// <summary>
        /// 降順ソートをして結果を返します。
        /// 破壊的関数です。
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="array"></param>
        /// <returns></returns>
        public static T[] SortDecend<T>(T[] array)
        {
            Array.Sort<T>(array);
            Array.Reverse(array);
            return array;
        }

        /// <summary>
        /// Rubyにあるようなやつ
        /// ex) 5.Times(i => Console.WriteLine(i));
        /// </summary>
        /// <param name="times"></param>
        /// <param name="action"></param>
        public static void Times(this int times, Action<int> action)
        {
            for (int i = 0; i < times; i++)
            {
                action(i);
            }
        }

        /// <summary>
        /// 引数aと引数bの値を入れ替えます
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="a"></param>
        /// <param name="b"></param>
        public static void Swap<T>(ref T a, ref T b)
        {
            T _a = a;
            a = b;
            b = _a;
        }

        /// <summary>
        /// Console.WriteLineの自動フラッシュをしないようにする
        /// </summary>
        public static void DontAutoFlush()
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
        }

        public static void Flush()
        {
            Console.Out.Flush();
        }

        /// <summary>
        /// 先頭と末尾に要素を増やした新しい配列を返します。
        /// </summary>
        /// <typeparam name="T"></typeparam>
        /// <param name="array"></param>
        /// <returns></returns>
        public static T[] AddHeadAndTail<T>(T[] array)
        {
            int len = array.Length;
            T[] res = new T[len + 2];
            Array.Copy(array, 0, res, 1, len);
            return res;
        }

        /// <summary>
        /// 昇順ソート済みの配列を2分探索します。
        /// 要素が見つからなかった場合はnより大きい数値の中で最小の数値のインデックスを返す。
        /// </summary>
        /// <param name="array"></param>
        /// <param name="n"></param>
        /// <returns></returns>
        public static int BinarySearch(long[] array, long n)
        {
            int left = 0;
            int right = array.Length - 1;

            while (left <= right)
            {
                int mid = (right - left) / 2 + left;

                if (array[mid] == n)
                {
                    return mid;
                }
                else if (n < array[mid])
                {
                    right = mid - 1;
                }
                else
                {
                    left = mid + 1;
                }
            }

            return left;
        }

        public static int GCD(int a, int b)
        {
            return (b == 0) ? a : GCD(b, a % b);
        }

        public static int[] GetDivisor(int n)
        {
            double sqrt = Math.Sqrt(n);

            List<int> divisor = new List<int>();

            for (int i = 1; i <= sqrt; i++)
            {
                if (n % i == 0)
                {
                    divisor.Add(i);
                    int tmp = n / i;
                    if (tmp != i)
                    {
                        divisor.Add(tmp);
                    }
                }
            }

            return Sort(divisor.ToArray());
        }

        public static int[] LongToBinaryArray(long n)
        {
            List<int> lst = new List<int>();

            while (n > 0)
            {
                int amari = (int)(n % 2);
                lst.Add(amari);
                n /= 2;
            }

            return lst.ToArray();
        }

        public static long BinaryArrayToLong(int[] binaryArray)
        {
            long result = 0;
            long b = 1;
            int len = binaryArray.Length;

            for (int i = 0; i < len; i++)
            {
                result += binaryArray[i] * b;
                b *= 2;
            }

            return result;
        }

        public static void Deconstruct<T>(this T[] items, out T t0)
        {
            t0 = items.Length > 0 ? items[0] : default(T);
        }

        public static void Deconstruct<T>(this T[] items, out T t0, out T t1)
        {
            if (items.Length < 2)
                throw new ArgumentException();

            t0 = items[0];
            t1 = items[1];
        }

        public static void Deconstruct<T>(this T[] items, out T t0, out T t1, out T t2)
        {
            if (items.Length < 3)
                throw new ArgumentException();

            t0 = items[0];
            t1 = items[1];
            t2 = items[2];
        }

        public static void Deconstruct<T>(this T[] items, out T t0, out T t1, out T t2, out T t3)
        {
            if (items.Length < 4)
                throw new ArgumentException();

            t0 = items[0];
            t1 = items[1];
            t2 = items[2];
            t3 = items[3];
        }

        public static void ArrayInitialize<T>(T[,] array, T value)
        {
            int len0 = array.GetLength(0);
            int len1 = array.GetLength(1);

            for (int i = 0; i < len0; i++)
            {
                for (int j = 0; j < len1; j++)
                {
                    array[i, j] = value;
                }
            }
        }

        public static void ChMax(ref long a, long b)
        {
            if (a < b) a = b;
        }

        public static void ChMin(ref long a, long b)
        {
            if (a > b) a = b;
        }

        public readonly static int MOD = 1000000007;
        public static void ModAdd(ref long a, long b)
        {
            a += b;
            if (a >= MOD)
                a %= MOD;
        }

        public static T MinBy<T>(this IEnumerable<T> source, Func<T, long> conv)
        {
            T min = source.First();
            long minValue = conv(min);
            foreach (T x in source.Skip(1))
            {
                long n = conv(x);
                if (n < minValue)
                {
                    min = x;
                }
            }

            return min;
        }

        public static T MaxBy<T>(this IEnumerable<T> source, Func<T, long> conv)
        {
            T min = source.First();
            long maxValue = conv(min);
            foreach (T x in source.Skip(1))
            {
                long n = conv(x);
                if (maxValue < n)
                {
                    min = x;
                }
            }

            return min;
        }
    }

    /// <summary>
    /// HashSetにTupleを入れた時の、等値性判定方法の指定に使います。
    /// HashSetのコンストラクタに渡して使います。
    /// EqualsとGetHashCodeを提供します。
    /// </summary>
    /// <typeparam name="T"></typeparam>
    public class EqualityComparer<T> : IEqualityComparer<T>
    {
        private Func<T, T, bool> _equals;
        private Func<T, int> _getHashCode;

        public EqualityComparer(Func<T, T, bool> equals, Func<T, int> getHashCode)
        {
            _equals = equals;
            _getHashCode = getHashCode;
        }

        public bool Equals(T x, T y)
        {
            return _equals(x, y);
        }

        public int GetHashCode(T obj)
        {
            return _getHashCode(obj);
        }
    }

    /// <summary>
    /// UnionFindTree
    /// </summary>
    public class UnionFindTree
    {
        public int[] Node;

        public UnionFindTree(int N)
        {
            Node = new int[N];
            for (int i = 0; i < N; i++)
            {
                Node[i] = -1;
            }
        }

        public bool IsSameGroup(int x, int y)
        {
            return GetRoot(x) == GetRoot(y);
        }

        public bool Merge(int x, int y)
        {
            int xr = GetRoot(x);
            int yr = GetRoot(y);

            if (xr == yr)
                return false;

            // xが、大きなグループを示すようにSwapする（値が小さい方が大きなグループ）
            if (Node[xr] > Node[yr])
                Swap(ref xr, ref yr);

            // グループの数を合算する
            Node[xr] += Node[yr];

            // 根を張り替える
            Node[yr] = xr;
            return true;
        }

        public int Size(int x)
        {
            return -Node[GetRoot(x)];
        }

        public int GetRoot(int n)
        {
            if (Node[n] < 0)
            {
                return n;
            }
            else
            {
                // 根を張りなおす。
                Node[n] = GetRoot(Node[n]);
                return Node[n];
            }
        }
    }

    /// <summary>
    /// PriorityQueue
    /// </summary>
    /// <typeparam name="T"></typeparam>
    public class PriorityQueue<T>
    {
        private Comparison<T> _comparison = null;
        private int _type = 0;

        private T[] _heap;
        private int _sz = 0;

        private int _count = 0;

        /// <summary>
        /// Priority queue
        /// </summary>
        /// <param name="maxSize">max size</param>
        /// <param name="type">0: asc, 1:desc</param>
        public PriorityQueue(int maxSize, int type = 0)
        {
            _heap = new T[maxSize];
            _type = type;
        }

        public PriorityQueue(int maxSize, Comparison<T> comparison)
        {
            _heap = new T[maxSize];
            _comparison = comparison;
        }

        private int Compare(T x, T y)
        {
            return _comparison(x, y);
            //if (_comparison != null) return _comparison(x, y);
            //return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
        }

        public void Push(T x)
        {
            _count++;

            //node number
            var i = _sz++;

            while (i > 0)
            {
                //parent node number
                var p = (i - 1) / 2;

                if (Compare(_heap[p], x) <= 0) break;

                _heap[i] = _heap[p];
                i = p;
            }

            _heap[i] = x;
        }

        public T Pop()
        {
            _count--;

            T ret = _heap[0];
            T x = _heap[--_sz];

            int i = 0;
            while (i * 2 + 1 < _sz)
            {
                //children
                int a = i * 2 + 1;
                int b = i * 2 + 2;

                if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

                if (Compare(_heap[a], x) >= 0) break;

                _heap[i] = _heap[a];
                i = a;
            }

            _heap[i] = x;

            return ret;
        }

        public int Count()
        {
            return _count;
        }

        public T Peek()
        {
            return _heap[0];
        }

        public bool Contains(T x)
        {
            for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
            return false;
        }

        public void Clear()
        {
            while (this.Count() > 0) this.Pop();
        }

        public IEnumerator<T> GetEnumerator()
        {
            var ret = new List<T>();

            while (this.Count() > 0)
            {
                ret.Add(this.Pop());
            }

            foreach (var r in ret)
            {
                this.Push(r);
                yield return r;
            }
        }

        public T[] ToArray()
        {
            T[] array = new T[_sz];
            int i = 0;

            foreach (var r in this)
            {
                array[i++] = r;
            }

            return array;
        }
    }
}