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.