—“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 $K$ ($1 \leq N \leq 100000$, $1 \leq K \leq 50$). The following line of input contains $N$ integers $a_ i$ ($0 \leq a_ i \leq 10^9$).

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

-----Examples-----
Sample Input 1:
5 3
2 4 2 3 4
Sample Output 1:
39

Sample Input 2:
5 1
1 0 1 1 1
Sample Output 2:
4

Source: kattis | Difficulty: HARD


Solutions: