Description

Input

The first line of input contains two integers $n$ and $k$, where $n$ is the number of elements in $A$ ($1\le k\le n\le 600$).

The second line of input contains $n$ integers $a_1,a_2,\dots,a_n$, describing the elements in $A$ ($-10^9\le a_i\le 10^9$).

Output

Output $\sum\limits_{B\subseteq A} f(B)$ modulo $10^9+7$.

3 2
-1 2 4

10

3 1
1 1 1

7

10 4
-24 -41 9 -154 -56 14 18 53 -7 120

225905161

15 5
0 0 2 -2 2 -2 3 -3 -3 4 5 -4 -4 4 5

18119684

Note

Consider the first sample. From the definitions we know that

• $f(\varnothing)=0$
• $f(\{-1\})=0$
• $f(\{2\})=0$
• $f(\{4\})=0$
• $f(\{-1,2\})=-2$
• $f(\{-1,4\})=-4$
• $f(\{2,4\})=8$
• $f(\{-1,2,4\})=8$

So we should print $(0+0+0+0-2-4+8+8)\bmod (10^9+7)=10$.

In the second example, note that although the multiset consists of three same values, it still has $8$ distinct subsets: $\varnothing,\{1\},\{1\},\{1\},\{1,1\},\{1,1\},\{1,1\},\{1,1,1\}$.