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 10^5

1 \leq w_i \leq W

1 \leq v_i \leq 10^9

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

5 5
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000

Sample Output 2

5000000000

The answer may not fit into a 32-bit integer type.

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.Numerics;
using System.Linq;
using static System.Math;

class MainClass
{

    public static void Main(string[] args)
    {
        var _ = LnInts();
        var N = _[0]; var W = _[1];
        var Vs = new long[N][];
        for (var i = 0; i < N; i++)
        {
            Vs[i] = LnLngs();
        }
        var dp = new long[N + 1][];
        for (int i = 0; i < dp.Length; i++)
        {
            dp[i] = new long[W + 1];
        }
        dp[0][1] = 0;
        for (int i = 0; i < N; i++)
        {
           
            for (int w = 0; w <= W; w++)
            {
                if (w >= Vs[i][0])
                {
                    dp[i + 1][w] = Max(dp[i][w], dp[i][w - Vs[i][0]] + Vs[i][1]);
                }
                dp[i + 1][w] = Max(dp[i + 1][w], dp[i][w]);
            }
        }
        Console.WriteLine(dp[N][W]);
    }

    public static long Gcd(long a, long b) { if (a > b) { var r = a % b; if (r == 0) return b; else return Gcd(b, r); } else { var r = b % a; if (r == 0) return a; else return Gcd(a, r); } }
    public static int Gcd(int a, int b) { if (a > b) { var r = a % b; if (r == 0) return b; else return Gcd(b, r); } else { var r = b % a; if (r == 0) return a; else return Gcd(a, r); } }
    public static int[] LnInts() { var vs = Console.ReadLine().Trim().Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries); var ins = new int[vs.Length]; for (int i = 0; i < vs.Length; i++) ins[i] = int.Parse(vs[i]); return ins; }
    public static int LnInt() { var vs = Console.ReadLine().Trim(); return int.Parse(vs); }
    public static long[] LnLngs() { var vs = Console.ReadLine().Trim().Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries); var ins = new long[vs.Length]; for (int i = 0; i < vs.Length; i++) ins[i] = long.Parse(vs[i]); return ins; }
    public static long LnLng() { var vs = Console.ReadLine().Trim(); return long.Parse(vs); }
    public static string[] LnStrs() { var vs = Console.ReadLine().Trim().Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries); return vs; }
    public static string LnStr() { var vs = Console.ReadLine().Trim(); return vs; }
}