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
MOD, ans = 10**9+7, 0
n, k = map(int, input().split())
a = list(map(int, input().split()))
a.sort()
kai, gai = [1], [1]
for i in range(n):
	kai.append((kai[i] * (i+1)) % MOD)
	gai.append(pow((kai[i] * (i+1)) % MOD, MOD-2, MOD))
for i in range(n):
	x, y = 0, 0
	if i <= (n-k):
		x = (a[i] * kai[n-i-1] * gai[n-i-k] * gai[k-1]) % MOD
	if i >= (k-1):
		y = (a[i] * kai[i] * gai[i-k+1] * gai[k-1]) % MOD
	ans = (ans + y - x) % MOD
print(ans)