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.

Constraints

* 1 ≤ N ≤ 40
* 1 ≤ vi ≤ 1015
* 1 ≤ wi ≤ 1015
* 1 ≤ W ≤ 1015

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.

Examples

Input

4 5
4 2
5 2
2 1
8 3


Output

13


Input

2 20
5 9
4 10


Output

9
import sys
from bisect import bisect_right


def meet_in_the_middle(a: list, limit: int) -> tuple:
    first_v, first_w, second_v, second_w = [], [], [], []
    for items, v_append, w_append in (
            (a[:len(a)//2], first_v.append, first_w.append),
            (a[len(a)//2:], second_v.append, second_w.append)
    ):
        enumerated = [(0, 0)]
        for v, w in items:
            enumerated += [(w+_w, v+_v) for _w, _v in enumerated]

        enumerated.sort()
        enumerated = enumerated[:bisect_right(enumerated, (limit, float("inf")))] + [(limit+1, 0)]
        max_v = -1
        for (cw, cv), (nw, nv) in zip(enumerated, enumerated[1:]):
            if cw < nw and max_v < cv:
                v_append(cv)
                w_append(cw)
                max_v = cv

    return (first_v, first_w), (second_v, second_w)


N, W = map(int, input().split())
a = [list(map(int, l.split())) for l in sys.stdin]

(first_v, first_w), (second_v, second_w) = meet_in_the_middle(a, W)
ans = 0
for v, w in zip(first_v, first_w):
    i = bisect_right(second_w, W-w)-1
    new_v = v + second_v[i]
    if ans < new_v:
        ans = new_v
print(ans)
