A8676 | 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 $1000000007$ $(10^{9}+7)$ .

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.

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