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 $\bmod (10^9+7)$.

Constraints

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

Input

Input is given from Standard Input in the following format:

N K
A_1 ... A_N

Output

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

Examples

Input

4 2
1 1 3 4

Output

11

Input

6 3
10 10 10 -10 -10 -10

Output

360

Input

3 1
1 1 1

Output

0

Input

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

Output

999998537

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