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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ATCoderPuzzles
{
    class DKnapsack1
    {
        static void Main()
        {
            // N, W
            var backpack = Console.ReadLine().Split(" ").Select(int.Parse).ToArray();

            // WeightRemaining, value
            SortedDictionary<int, long> dict = new SortedDictionary<int, long>(new CustomComparer())
            {
                { backpack[1], 0 }
            };
            Queue<KeyValuePair<int, long>> newPairs = new Queue<KeyValuePair<int, long>>();

            // Build set
            long maxVal = 0;
            while (backpack[0]-- > 0)
            {
                // Weight, Value
                int[] lineSegments = Console.ReadLine().Split(" ").Select(int.Parse).ToArray();

                // Build
                //PrintDict(dict);
                foreach (var val in dict)
                {
                    //Console.WriteLine($"Combining with [{val.Key},{val.Value}]");
                    int weightRemaining = val.Key - lineSegments[0];
                    if (weightRemaining >= 0)
                        newPairs.Enqueue(new KeyValuePair<int, long>(weightRemaining, lineSegments[1] + val.Value));
                    else
                        break;
                }

                // Add
                foreach (var entry in newPairs)
                {
                    maxVal = Math.Max(maxVal, AddOrUpdate(dict, entry.Key, entry.Value));
                }
            }

            Console.WriteLine(maxVal);
        }

        static void PrintDict(SortedDictionary<int, long> dict)
        {
            foreach (var entry in dict)
                Console.WriteLine($"\t[{entry.Key},{entry.Value}]");
        }

        static long AddOrUpdate(SortedDictionary<int, long> dict, int weightRemaining, long value)
        {
            if(dict.ContainsKey(weightRemaining))
            {
                if (dict[weightRemaining] < value)
                    dict[weightRemaining] = value;
            }
            else
            {
                dict.Add(weightRemaining, value);
            }
            return dict[weightRemaining];
        }
    }

    public class CustomComparer : IComparer<int>
    {
        public int Compare(int a, int b)
        {
            return b.CompareTo(a);
        }
    }
}