CF241B.Friends

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 (109 + 7).

你有 $n$ 个朋友，想要为他们拍摄 $m$ 张照片。每张照片中恰好出现两名朋友，且任意两张照片所包含的朋友对均不相同。因此，若你有 $n = 3$ 个朋友，则最多可拍摄 $3$ 张不同的照片，每张照片包含其中一对朋友。

每位朋友都有一个吸引力值，第 $i$ 位朋友的吸引力值为整数 $a_i$。已知包含第 $i$ 位和第 $j$ 位朋友的照片的吸引力值等于整数 $a_i$ 与 $a_j$ 的按位异或（即 xor 运算）结果。

你希望以某种方式拍摄照片，使得所有照片的吸引力值之和最大化。你需要计算该最大值。由于结果可能超出 32 位整数范围，请将结果对 $1000000007$（即 $10^9 + 7$）取模后输出。

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 ≤ 109) — the values of attractiveness of the friends.

输入的第一行包含两个整数 $n$ 和 $m$ —— 分别表示朋友的数量和你想拍摄的照片数量。

下一行包含 $n$ 个用空格分隔的整数 $a_1,\ a_2,\ \dots,\ a_n$（$0\le a_i\le 10^9$）—— 表示各位朋友的吸引力值。

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

输出仅有一行，应包含一个整数——即你所选照片的吸引力总和的最大值。