Codeforces Round 743 (Div. 1) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

flows

graph matchings

graphs

greedy

*2800

No tag edit access

The problem statement has recently been changed. View the changes.

×
D. Bridge Club

time limit per test

2.5 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputThere are currently $$$n$$$ hot topics numbered from $$$0$$$ to $$$n-1$$$ at your local bridge club and $$$2^n$$$ players numbered from $$$0$$$ to $$$2^n-1$$$. Each player holds a different set of views on those $$$n$$$ topics, more specifically, the $$$i$$$-th player holds a positive view on the $$$j$$$-th topic if $$$i\ \&\ 2^j > 0$$$, and a negative view otherwise. Here $$$\&$$$ denotes the bitwise AND operation.

You are going to organize a bridge tournament capable of accommodating at most $$$k$$$ pairs of players (bridge is played in teams of two people). You can select teams arbitrarily while each player is in at most one team, but there is one catch: two players cannot be in the same pair if they disagree on $$$2$$$ or more of those $$$n$$$ topics, as they would argue too much during the play.

You know that the $$$i$$$-th player will pay you $$$a_i$$$ dollars if they play in this tournament. Compute the maximum amount of money that you can earn if you pair the players in your club optimally.

Input

The first line contains two integers $$$n$$$, $$$k$$$ ($$$1 \le n \le 20$$$, $$$1 \le k \le 200$$$) — the number of hot topics and the number of pairs of players that your tournament can accommodate.

The second line contains $$$2^n$$$ integers $$$a_0, a_1, \dots, a_{2^n-1}$$$ ($$$0 \le a_i \le 10^6$$$) — the amounts of money that the players will pay to play in the tournament.

Output

Print one integer: the maximum amount of money that you can earn if you pair the players in your club optimally under the above conditions.

Examples

Input

3 1 8 3 5 7 1 10 3 2

Output

13

Input

2 3 7 4 5 7

Output

23

Input

3 2 1 9 1 5 7 8 1 1

Output

29

Note

In the first example, the best we can do is to pair together the $$$0$$$-th player and the $$$2$$$-nd player resulting in earnings of $$$8 + 5 = 13$$$ dollars. Although pairing the $$$0$$$-th player with the $$$5$$$-th player would give us $$$8 + 10 = 18$$$ dollars, we cannot do this because those two players disagree on $$$2$$$ of the $$$3$$$ hot topics.

In the second example, we can pair the $$$0$$$-th player with the $$$1$$$-st player and pair the $$$2$$$-nd player with the $$$3$$$-rd player resulting in earnings of $$$7 + 4 + 5 + 7 = 23$$$ dollars.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/06/2024 00:59:02 (g1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|