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)

// AOJ DPL_1_H Huge Knapsack Problem
// 2018.5.11 bal4u
 
#include <stdio.h>
#include <stdlib.h>

#if 1
#define gc() getchar_unlocked()
#else
#define gc() getchar()
#endif
 
int in()
{
    int n = 0, c = gc();
    do n = 10*n + (c & 0xf), c = gc(); while (c >= '0');
    return n;
}

long long inLL()
{
    long long n = 0, c = gc();
    do n = 10*n + (c & 0xf), c = gc(); while (c >= '0');
    return n;
}

#define MAX  ((1<<20)+5)

typedef struct { long long v, w; } TBL;
TBL a[42];
TBL a1[MAX]; int c1, c2;

long long binarysearch_upper(long long x)
{
	int m, l = 0, r = c2;

    while (l < r) {
        m = (l+r) >> 1;
		if (a1[m].w <= x) l = m + 1; else r = m;
    }
	return a1[l-1].v;
}

int cmp(TBL *a, TBL *b)
{
	if (a->w == b->w) {
		if (a->v > b->v) return -1;
		return (a->v < b->v);
	}
	if (a->w < b->w) return -1;
	return (a->w > b->w);
}

int main()
{
	int N, i, j, m1, m2, lim;
	long long W, x, y, t, ans;

	N = in(), W = inLL();

	for (i = 0; i < N; i++) a[i].v = inLL(), a[i].w = inLL();

	m1 = N / 2, lim = 1 << m1;
	c1 = 0; for (i = 0; i < lim; i++) {
		x = 0, y = 0;
		for (j = 0; j < m1; j++) {
			if ((i >> j) & 1) {
				x += a[j].v;
				y += a[j].w;
			}
		}
		if (y <= W) {
			a1[c1  ].v = x; 
			a1[c1++].w = y;
		}
	}

	qsort(a1, c1, sizeof(TBL), cmp);

	c2 = 1;
	for (i = 1; i < c1; i++) {
		if (a1[c2-1].v < a1[i].v) a1[c2++] = a1[i];
	}

	ans = 0;
	m2 = N - m1, lim = 1 << m2;
	for (i = 0; i < lim; i++) {
		x = 0, y = 0;
		for (j = 0; j < m2; j++) {
			if ((i >> j) & 1) {
				x += a[m1+j].v;
				y += a[m1+j].w;
			}
		}
		if (y <= W) {
			t = x + binarysearch_upper(W-y);
			if (t > ans) ans = t;
		}
	}
	printf("%lld\n", ans);
	return 0;
}