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
n, k = map(int, input().split())
a_list = list(map(int, input().split()))
a_list.sort()


mod = 10 ** 9 + 7
f_list = [1]
for i in range(1,n+1):
    f_list.append((f_list[-1] * i) % mod)
def comb(n,r):
    return f_list[n] * (pow(f_list[r], mod-2, mod) * pow(f_list[n-r], mod-2, mod) % mod) % mod


max_val = 0
min_val = 0
for i in range(n - k + 1):
    val = comb(n - i - 1, k - 1)
    max_val = (max_val + (((a_list[-(i + 1)]) * val))) % (10 ** 9 + 7)
    min_val = (min_val + ((a_list[i]) * val)) % (10 ** 9 + 7)

print(int((max_val - min_val) % (10 ** 9 + 7)))