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 = 10**9+7
n, k = [ int(v) for v in input().split() ]
num = sorted([ int(v) for v in input().split() ])


max_list2 = [ (i, i-k+1) for i in range(n) ]
max_list = []
for a, b in max_list2:
    if b < 0:
        max_list.append(0)
    elif b == 0:
        max_list.append(1)
    else:
        s = max_list[-1]
        s *= a * pow(b, mod-2, mod)
        max_list.append(s%mod)

min_list = list(reversed(max_list))

max_min_list = [ (max_list[i] - min_list[i]) * num[i] for i in range(n) ] 
print(sum(max_min_list) % mod)