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;
class Program
{
	//static long[,] dp;
	//static	List<List<long>> dp;
	static int[] weight, value;
    //static List<string> str = new List<string>();
	static void Main(string[] args)
	{
		// 入力フェーズ
		//int N = Int32.Parse(Console.ReadLine()); // 夏休みの日数
		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、重さの総和がW以下になるように選んだ時の価値の総和の最大値
		/*dp = new long[N+1,W+1];
		dp = new List<List<long>>();
		for(int i=0; i<=N; i++)
		{
			List<long> l = new List<long>();
			for(int j=0; j<=W; j++)
			{
				l.Add(0);
			}
			dp.Add(l);
		}
		// 数値型をnewすると全て0で初期化されるので、0を初期値とし
		// 0を代入するときには-1を入れる。（以降0として扱う）（逆におそくなる？？
*/
// dp[N, W] から再帰的に求めて行く（N*Wのマスを網羅せずにすむ）

		//getValue(N, W);

		/*for(int i=0; i<=N; i++)
		{
			for(int j=0; j<=W; j++)
			{
				Console.Write(dp[i][j] + " ");
			}
			Console.WriteLine();
		}
		*/
		//long maxHappy = Math.Max(dp[N,0], Math.Max(dp[N,1], dp[N,2]));
		Console.WriteLine(getValue(N,W) + "");

    }

		static long getValue(int i, int j)
		{
				// dp[i-1][j-weight[i-1]] + value[i-1]
				// dp[i-1][j]　の大きい方を返す
//Console.Write(i + ", " + j + " ");
		// 初期値
				if (i == 0 || j == 0) {
					return 0;
				}

				if(j-weight[i-1] < 0)
				{
					return getValue(i-1, j);
				}
				else {
					return Math.Max(
											getValue(i-1, j-weight[i-1]) + value[i-1]
											, getValue(i-1, j)
					);
				}
		}

}