B. Friends

B. Friends
time limit per test: 6 seconds
memory limit per test: 256 megabytes
input: standard input
output: standard output

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).

Input

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 a₁, a₂, ..., a_n (0 ≤ a_i ≤ 10⁹) — the values of attractiveness of the friends.

Output

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

Sample test(s)

input

3 1
1 2 3

output

3

input

3 2
1 2 3

output

5

input

3 3
1 2 3

output

6