Score : 500 points
For a finite set of integers X, let f(X)=\max X - \min X.
Given are N integers A_1,...,A_N.
We will choose K of them and let S be the set of the integers chosen. If we distinguish elements with different indices even when their values are the same, there are {}_N C_K ways to make this choice. Find the sum of f(S) over all those ways.
Since the answer can be enormous, print it \bmod (10^9+7).
Input is given from Standard Input in the following format:
N K A_1 ... A_N
Print the answer \bmod (10^9+7).
4 2 1 1 3 4
11
There are six ways to choose S: \{1,1\},\{1,3\},\{1,4\},\{1,3\},\{1,4\}, \{3,4\} (we distinguish the two 1s). The value of f(S) for these choices are 0,2,3,2,3,1, respectively, for the total of 11.
6 3 10 10 10 -10 -10 -10
360
There are 20 ways to choose S. In 18 of them, f(S)=20, and in 2 of them, f(S)=0.
3 1 1 1 1
0
10 6 1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0
999998537
Print the sum \bmod (10^9+7).