Problem:
Huge Knapsack Problem

You have N items that you want to put them into a knapsack. Item i has value vi and weight wi.

You want to find a subset of items to put such that:

The total value of the items is as large as possible.

The items have combined weight at most W, that is capacity of the knapsack.

Find the maximum total value of items in the knapsack.

Input

N W
v1 w1
v2 w2
:
vN wN

The first line consists of the integers N and W. In the following N lines, the value and weight of the i-th item are given.

Output

Print the maximum total values of the items in a line.

Constraints

1 ≤ N ≤ 40

1 ≤ vi ≤ 1015

1 ≤ wi ≤ 1015

1 ≤ W ≤ 1015

Sample Input 1

4 5
4 2
5 2
2 1
8 3

Sample Output 1

13

Sample Input 2

2 20
5 9
4 10

Sample Output 2

9

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using static System.Console;
using static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;
using System.Text;
class Program
{
    private static void chmin<T>(ref T num, T val) where T : IComparable<T>
        => num = num.CompareTo(val) == 1 ? val : num;
    private static void chmax<T>(ref T num, T val) where T : IComparable<T>
        => num = num.CompareTo(val) == -1 ? val : num;
    static void Main(string[] args)
    {
        var pr = new Program();
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        pr.Solve();
        Console.Out.Flush();
    }
    void Solve()
    {
        int num;
        long w;
        Input.Make(out num, out w);
        var vw = Input.arL2D(num);
        var ar = new[] { vw.Take(num / 2).ToArray(), vw.Skip(num / 2).ToArray() };
        var dic = new[] { new Dictionary<long, long>(), new Dictionary<long, long>() };
        for(var i=0;i<2;i++)
            for(var j=0;j<(1<<ar[i].Length);j++)
            {
                var sum = 0L;
                var val = 0L;
                for (var k = 0; k < ar[i].Length; k++)
                    if ((1 & j >> k) == 1)
                    {
                        if (sum > w) break;
                        sum += ar[i][k][1];
                        val += ar[i][k][0];
                    }
                if (sum > w) continue;
                if (!dic[i].ContainsKey(sum))
                    dic[i][sum] = 0;
                dic[i][sum]=Max(dic[i][sum],val);
            }
        var max = 0L;
        var list1 = dic[0].OrderByDescending(v => v.Key).ToArray();
        var list2 = dic[1].OrderBy(v => v.Key).ToArray();
        var index = 0;var submax = 0L;
        for(var i = 0; i < list1.Length; i++)
        {
            while (index != list2.Length && list2[index].Key + list1[i].Key <= w)
            {
                chmax(ref submax, list2[index].Value);
                index++;
            }
            chmax(ref max, submax + list1[i].Value);
        }
        while (index != list2.Length)
            chmax(ref max, list2[index++].Value);
        WriteLine(max);
    }
}

public class Input
{
    public static string read => ReadLine().Trim();
    public static int[] ar => read.Split(' ').Select(int.Parse).ToArray();
    public static int num => ToInt32(read);
    public static long[] arL => read.Split(' ').Select(long.Parse).ToArray();
    public static long numL => ToInt64(read);
    public static T[] create<T>(int n, Func<int, T> f)
        => Enumerable.Repeat(0, n).Select(f).ToArray();
    public static char[][] gred(int h)
        => create(h, _ => read.ToCharArray());
    public static int[] ar1D(int n)
        => create(n, _ => num);
    public static long[] arL1D(int n)
        => create(n, _ => numL);
    public static string[] strs(int n)
        => create(n, _ => read);
    public static int[][] ar2D(int n)
        => create(n, _ => ar);
    public static long[][] arL2D(int n)
        => create(n, _ => arL);
    public static List<T>[] edge<T>(int n)
        => create(n, _ => new List<T>());
    public static T GetValue<T>(string g)
    {
        var t = typeof(T);
        if (t == typeof(int))
            return (T)(object)int.Parse(g);
        if (t == typeof(long))
            return (T)(object)long.Parse(g);
        if (t == typeof(string))
            return (T)(object)g;
        if (t == typeof(char))
            return (T)(object)char.Parse(g);
        if (t == typeof(double))
            return (T)(object)double.Parse(g);
        if (t == typeof(bool))
            return (T)(object)bool.Parse(g);
        return default(T);
    }
    public static void Make<T1, T2>(out T1 v1, out T2 v2)
    {
        v1 = Next<T1>();
        v2 = Next<T2>();
    }
    public static void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3)
    {
        Make(out v1, out v2);
        v3 = Next<T3>();
    }
    public static void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4)
    {
        Make(out v1, out v2, out v3);
        v4 = Next<T4>();
    }
    public static void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5)
    {
        Make(out v1, out v2, out v3, out v4);
        v5 = Next<T5>();
    }
    public static void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6)
    {
        Make(out v1, out v2, out v3, out v4, out v5);
        v6 = Next<T6>();
    }
    private static Queue<string> sc;
    public static T Next<T>(){ sc = sc ?? new Queue<string>(); if (sc.Count == 0) foreach (var item in read.Split(' ')) sc.Enqueue(item);return GetValue<T>(sc.Dequeue()); }
    public static void Next<T>(ref T val) => val = Next<T>(); 
    public const long Inf = (long)1e18;
    public const double eps = 1e-6;
    public const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public const int MOD = 1000000007;
}