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 = sorted([int(a) for a in input().split()])
P = 10**9+7

fa = [1]
for i in range(1, N + 2): fa.append(fa[-1] * i % P)
fainv = [pow(fa[-1], P-2, P)]
for i in range(1, N + 2)[::-1]: fainv.append(fainv[-1] * i % P)
fainv = fainv[::-1]

C = lambda a, b: fa[a] * fainv[b] * fainv[a-b] if 0 <= b <= a else 0
print(sum([(C(i, K-1) - C(N-i-1, K-1)) * A[i] % P for i in range(N)]) % P)