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.Linq;
using System.Text;
using System.Threading.Tasks;

namespace EDPCE2
{
    class Program
    {
        struct wv
        {
            public int weight;
            public int value;
        }
        static void Main(string[] args)
        {
            // スペース区切りの整数の入力
            string[] inputNW = Console.ReadLine().Split(' ');
            int N = int.Parse(inputNW[0]);
            long W = long.Parse(inputNW[1]);
            List<wv> Stock = new List<wv>();
            //long[] w = new long[N + 1];//重さ
            //int[] v = new int[N + 1];//価値
            wv article = new wv();
            int row = 0;
            article.weight = 0;
            article.value = 0;
            Stock.Add(article);//0番目の品物
            for (int i = 1; i <= N; i++)
            {
                string[] inputWV = Console.ReadLine().Split(' ');
                article.weight = int.Parse(inputWV[0]);
                article.value = int.Parse(inputWV[1]);
                Stock.Add(article);
                row += article.value;//DPの列の大きさ
            }
            if (N == 1)
            {
                if (Stock[1].weight <= W)
                {
                    Console.WriteLine(Stock[1].value);
                }
                else
                {
                    Console.WriteLine(0);
                }
            }
            else
            {
                //同じ重さならvalueの大きい方を使いたい
                Stock.Sort((a, b) => b.value - a.value);
                Stock.Sort((a, b) => a.weight - b.weight);
                /*
                            foreach (var item in Stock)
                            {
                                Console.WriteLine(item.weight+" "+item.value);
                            }
                */
                int ans = 0;
                int max = (int)Math.Pow(10, 9) + 7;//大きな数字
                int[,] DP = new int[N + 1, row + 1];
                for (int i = 1; i <= row; i++)
                {
                    DP[0, i] = max;
                }
                for (int i = 1; i <= N; i++)//各品物を表す行
                {
                    for (int j = 1; j <= row; j++)//選んだ品物の価値の合計を表す列
                    {
                        if (Stock[i].value >= j)//選んだ品物の価値がＶより大きいなら
                        {
                            DP[i, j] = Math.Min(DP[i - 1, j], Stock[i].weight);
                        }
                        else//選んだ品物の価値ではＶに足りないなら
                        {
                            DP[i, j] = Math.Min(DP[i - 1, j], DP[i - 1, j - Stock[i].value] + Stock[i].weight);
                        }
                        //Console.Write(DP[i, j] + " ");
                        if ((DP[i, j] != max) && (DP[i, j] > W))
                        {
                            ans = j - 1;
                            break;
                        }
                    }
                    //Console.WriteLine();
                    if (ans != 0) break;
                }
                Console.WriteLine(ans);
            }
        }
    }
}