Problem A
Perica

—“I’m stopping by Žnidaršić’s house, you play the piano, Perica.”
—“Ok, dad, I will!”

And so, Perica began playing the piano. His piano consists of $N$ keys. Each key has a value written on it, $a_i$. When Perica plays the piano, he presses exactly $K$ different keys at the same time. The piano is a bit strange because, after pressing $K$ keys at the same time, it will play only the key with the largest value. Perica is going to play each combination of $K$ keys on the piano and he wants to know the sum of values of the keys that will be played.

Help Perica determine the remainder of that number modulo $1000000007$.

Input

The first line of input contains two integers $N$ and $K$ ($1\le N\le 100000$, $1\le K\le 50$). The following line of input contains $N$ integers $a_i$ ($0\le a_i\le {10}^9$).

Output

The first and only line of output must contain the required number from the task.

5 3
2 4 2 3 4

39

5 1
1 0 1 1 1

4

5 2
3 3 4 0 0

31