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;
class Program
{
	static long[,] dp;
	//static	List<List<long>> dp;
	static int[] weight, value;
	static long INF_LONG = long.MaxValue/2;
    //static List<string> str = new List<string>();
	static void Main(string[] args)
	{
		// 入力フェーズ
		//int N = Int32.Parse(Console.ReadLine());
		string[] input = Console.ReadLine().Split(' '); // N,W
		int N = Int32.Parse(input[0]);
		int W = Int32.Parse(input[1]);
		weight = new int[N];
		value = new int[N]; // 重さと価値の入力値
		for(int i=0; i<N; i++){
			string[] items = Console.ReadLine().Split(' ');
			weight[i] = Int32.Parse(items[0]);
			value[i] = Int32.Parse(items[1]);
		}
//Console.WriteLine(weight[0] + "");

//i番目までの品物のうち、価値の総和がj以上になるように選んだ時の重さの総和の最小値
		dp = new long[N+1,N*1000+1];
		for(int i=1; i<=N; i++)
		{
			for(int j=0; j<=N*1000; j++)
			{
				dp[i,j] = INF_LONG; //大きい数で初期化する
			}
		}
		HashSet<int> hs = new HashSet<int>();
		hs.Add(0);
		for(int i=1; i<=N; i++)
		{
			// i番目までの品物から選ぶ
			HashSet<int> loopHs = new HashSet<int>(hs);
			hs.Clear();
			foreach(int j in loopHs)
			{
				// i番目の品物を選ばない場合→価値の総和も重さの総和も変わらず(i-1と)
				dp[i,j] = Math.Min(dp[i-1, j], dp[i,j]); // 更新した方が小さくなるなら更新する

				hs.Add(j);

				// 選ぶ場合→価値も重さも増える
				// もし重さが制限を超えるようなら考慮する必要ないのでスルーする
				long ww = dp[i-1,j] + weight[i-1];

				if(ww > W)
				{
					continue;
				}
				else
				{
					dp[i, j+value[i-1]] = Math.Min(ww, dp[i,j+value[i-1]]);
					hs.Add(j+value[i-1]);
				}
			}

		}

		// N番目までの品物から選んで、価値の大きい順に見ていってW以下になったところの価値を表示する
		for(int j=N*1000; j>=0; j--)
		{
			if(dp[N, j] <= W)
				{
					Console.WriteLine(j + "");
					return;
				}
		}
  }
}