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 a 1, a 2, ..., 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.

Examples
Input
3 11 2 3
Output
3
Input
3 21 2 3
Output
5
Input
3 31 2 3
Output
6