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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.IO;
using static System.Math;
using static _20200218.Cin;
using static _20200218.Util;
using Pair = _20200218.VTuple<long, long>;

namespace _20200218
{
    public class Program
    {
        public static void Main(string[] args)
        {
            // A(); 15m
            // B(); 21m
            // C(); 32m
            // D(); 43m
            E();
        }

        public static void E()
        {
            long N = rl;
            long W = rl;
            long[] w, v;
            ReadCols(out w, out v, N);
            long MAX_V = 1000 * N;
            long[,] dp = new long[N + 1, MAX_V + 1];
            FillArray(dp, INF);
            dp[0, 0] = 0;
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < MAX_V; j++)
                {
                    if(j - v[i] < 0)
                        dp[i + 1, j] = dp[i, j];
                    else
                    {
                        dp[i + 1, j] = Min(dp[i, j], dp[i, j - v[i]] + w[i]);
                    }
                }
            }

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

            Console.WriteLine(ans);
        }

        public static void D()
        {
            long N = rl;
            long W = rl;
            long[] w, v;
            ReadCols(out w, out v, N);
            long[,] dp = new long[N + 1, W + 1];
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j <= W; j++)
                {
                    if (j - w[i] < 0)
                    {
                        dp[i + 1, j] = dp[i, j];
                    }
                    else
                    {
                        dp[i + 1, j] = Max(dp[i, j], dp[i, j - w[i]] + v[i]);
                    }
                }                
            }
            Console.WriteLine(dp[N, W]);
        }

        public static void C()
        {
            long N = rl;
            long[] a, b, c;
            ReadCols(out a, out b, out c, N);

            long[,] dp = new long[N+1, 3];
            for (int i = 0; i < N; i++)
            {
                dp[i + 1, 0] = Max(dp[i, 1], dp[i, 2]) + a[i];
                dp[i + 1, 1] = Max(dp[i, 0], dp[i, 2]) + b[i];
                dp[i + 1, 2] = Max(dp[i, 0], dp[i, 1]) + c[i];
            }

            long ans = Max(dp[N, 0], Max(dp[N, 1], dp[N, 2]));
            Console.WriteLine(ans);
        }

        public static void B()
        {
            long N = rl;
            long K = rl;
            long[] A = rla;
            long[] dp = new long[N];
            FillArray(dp, INF);
            dp[0] = 0;
            for (int i = 0; i < N - 1; i++)
            {
                for (int j = 1; j <= K && i + j < N; j++)
                {
                    dp[i + j] = Min(dp[i + j], dp[i] + Abs(A[i + j] - A[i]));
                }
            }

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

        public static void A()
        {
            long N = rl;
            long[] A = rla;

            long[] dp = new long[N];
            FillArray(dp, INF);
            dp[0] = 0;
            for (int i = 0; i < N - 1; i++)
            {
                dp[i + 1] = Min(dp[i + 1], dp[i] + Abs(A[i + 1] - A[i]));
                if (i + 2 < N)
                    dp[i + 2] = dp[i] + Abs(A[i + 2] - A[i]);
            }

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

    public class HashMap<K,V>:Dictionary<K,V>{V i;static Func<V>j=System.Linq.Expressions.Expression.Lambda<Func<V>>(System.Linq.Expressions.Expression.New(typeof(V))).Compile();public HashMap(){}public HashMap(V a){i=a;}new public V this[K a]{get{V b;if(TryGetValue(a,out b))return b;else return base[a]=i!=null?i:j();}set{base[a]=value;}}}public static class Util{public static readonly long INF=(long)1e17;public readonly static long MOD=(long)1e9+7;public static void DontAutoFlush(){var a=new System.IO.StreamWriter(Console.OpenStandardOutput()){AutoFlush=false};Console.SetOut(a);}public static void Flush(){Console.Out.Flush();}public static T[]Sort<T>(T[]a){Array.Sort<T>(a);return a;}public static T[]SortDecend<T>(T[]a){Array.Sort<T>(a);Array.Reverse(a);return a;}public static void Swap<T>(ref T a,ref T b){T c=a;a=b;b=c;}public static int GCD(int a,int b){return(b==0)?a:GCD(b,a%b);}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 static long ModAdd(long a,long b){long c=a+b;if(c>=MOD)return c%MOD;return c;}public static long ModMul(long a,long b){long c=a*b;if(c>=MOD)return c%MOD;return c;}public static void ChModAdd(ref long a,long b){a+=b;if(a>=MOD)a%=MOD;}public static void ChModMul(ref long a,long b){a*=b;if(a>=MOD)a%=MOD;}public static void FillArray<T>(T[]a,T b){int c=a.Length;for(int d=0;d<c;d++)a[d]=b;}public static void FillArray<T>(T[,]a,T b){int c=a.GetLength(0);int d=a.GetLength(1);for(int e=0;e<c;e++)for(int f=0;f<d;f++){a[e,f]=b;}}public static void FillArray<T>(T[,,]a,T b){int c=a.GetLength(0);int d=a.GetLength(1);int e=a.GetLength(2);for(int f=0;f<c;f++)for(int g=0;g<d;g++){for(int h=0;h<e;h++){a[f,g,h]=b;}}}public static long[]Accumulate(long[]a){long[]b=new long[a.Length+1];for(int c=0;c<a.Length;c++)b[c+1]=b[c]+a[c];return b;}public static double[]Accumulate(double[]a){double[]b=new double[a.Length+1];for(int c=0;c<a.Length;c++)b[c+1]=b[c]+a[c];return b;}}public static class Cin{public static long rl{get{return ReadLong();}}public static long[]rla{get{return ReadLongArray();}}public static double rd{get{return ReadDouble();}}public static double[]rda{get{return ReadDoubleArray();}}public static string rs{get{return ReadString();}}public static int ReadInt(){return int.Parse(k());}public static long ReadLong(){return long.Parse(k());}public static double ReadDouble(){return double.Parse(k());}public static string ReadString(){return k();}public static int[]ReadIntArray(){i=null;return Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);}public static long[]ReadLongArray(){i=null;return Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);}public static double[]ReadDoubleArray(){i=null;return Array.ConvertAll(Console.ReadLine().Split(' '),double.Parse);}public static void ReadCols(out long[]a,out long[]b,long c){a=new long[c];b=new long[c];for(int d=0;d<c;d++){a[d]=ReadLong();b[d]=ReadLong();}}public static void ReadCols(out long[]a,out long[]b,out long[]c,long d){a=new long[d];b=new long[d];c=new long[d];for(int e=0;e<d;e++){a[e]=ReadLong();b[e]=ReadLong();c[e]=ReadLong();}}public static int[][]ReadIntTable(int a){i=null;int[][]b=new int[a][];for(int c=0;c<a;c++)b[c]=ReadIntArray();return b;}public static long[][]ReadLongTable(long a){i=null;long[][]b=new long[a][];for(long c=0;c<a;c++)b[c]=ReadLongArray();return b;}static string[]i{get;set;}static int j{get;set;}static string k(){if(i==null||i.Length<=j){i=Console.ReadLine().Split(' ');j=0;}return i[j++];}}public struct VTuple<T1,T2>:IComparable<VTuple<T1,T2>>,IEquatable<VTuple<T1,T2>>{public T1 First;public T2 Second;public VTuple(T1 a,T2 b){First=a;Second=b;}public int CompareTo(VTuple<T1,T2>a){int b=Comparer<T1>.Default.Compare(First,a.First);if(b!=0)return b;return Comparer<T2>.Default.Compare(Second,a.Second);}public override bool Equals(object a){return a is VTuple<T1,T2>&&Equals((VTuple<T1,T2>)a);}public bool Equals(VTuple<T1,T2>a){return EqualityComparer<T1>.Default.Equals(First,a.First)&&EqualityComparer<T2>.Default.Equals(Second,a.Second);}public override int GetHashCode(){int a=First!=null?First.GetHashCode():0;int b=Second!=null?Second.GetHashCode():0;uint c=((uint)a<<5)|((uint)a>>27);return((int)c+a)^b;}}
}