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B. Friends

time limit per test

6 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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).

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} ≤ 10^{9}) — 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 1

1 2 3

Output

3

Input

3 2

1 2 3

Output

5

Input

3 3

1 2 3

Output

6

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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