Problem Statement

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

Input is given from Standard Input in the following format:
N K
A_1 ... A_N

Output

Print the answer $\bmod (10^9+7)$.

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq K \leq N$
• $|A_i| \leq 10^9$

Sample Input 1

4 2
1 1 3 4

Sample Output 1

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.

Sample Input 2

6 3
10 10 10 -10 -10 -10

Sample Output 2

360

There are 20 ways to choose S. In 18 of them, f(S)=20, and in 2 of them, f(S)=0.

Sample Input 3

3 1
1 1 1

Sample Output 3

0

Sample Input 4

10 6
1000000000 1000000000 1000000000 1000000000 1000000000 0 0 0 0 0

Sample Output 4

999998537

Print the sum $\bmod (10^9+7)$.

见题面 Input 部分

见题面 Output 部分