Friends

题意翻译

给定n个整数$a1,a2...an$,求两两异或值前k大的和。 其中$n<=50000,ai<=10^9$。答案对$1000000007 (10^9+7)$取模。

题目描述

You have $ n $ friends and you want to take $ m $ pictures of them. Exactly two of your friends should appear in each picture and no two pictures should contain the same pair of your friends. So if you have $ n=3 $ friends you can take $ 3 $ different pictures, each containing a pair of your friends. Each of your friends has an attractiveness level which is specified by the integer number $ a_{i} $ for the $ i $ -th friend. You know that the attractiveness of a picture containing the $ i $ -th and the $ j $ -th friends is equal to the exclusive-or ( $ xor $ operation) of integers $ a_{i} $ and $ a_{j} $ . You want to take pictures in a way that the total sum of attractiveness of your pictures is maximized. You have to calculate this value. Since the result may not fit in a 32-bit integer number, print it modulo $ 1000000007 $ $ (10^{9}+7) $ .

输入输出格式

输入格式

The first line of input contains two integers $ n $ and $ m $  — the number of friends and the number of pictures that you want to take. Next line contains $ n $ space-separated integers $ a_{1},a_{2},...,a_{n} $ ( $ 0<=a_{i}<=10^{9} $ ) — the values of attractiveness of the friends.

输出格式

The only line of output should contain an integer — the optimal total sum of attractiveness of your pictures.

输入输出样例

输入样例 #1

3 1
1 2 3

输出样例 #1

3

输入样例 #2

3 2
1 2 3

输出样例 #2

5

输入样例 #3

3 3
1 2 3

输出样例 #3

6