Max-Min Sums

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

inputFormat

Input

Input is given from Standard Input in the following format:

N K A_1 ... A_N

outputFormat

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

样例

3 1
1 1 1

0