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(map(int, input().split()))
A.sort()
m = 10**9 + 7

a = [None] * (N+1)
inva = [None] * (N+1)
a[0] = 1

for i in range(1, N+1):
    a[i] = i * a[i-1] % m

inva[N] = pow(a[N],m-2,m)
for i in range(N):
    inva[N-i-1] = inva[N-i] * (N-i) % m

ans = 0
for i in range(N):
    if i < K-1: continue
    tmp = (a[i] * inva[i-K+1] % m) * inva[K-1] % m 
    ans += A[i] * tmp
    ans %= m

for i in range(N):
    if i > N-K: continue
    tmp = (a[N-1-i] * inva[N-K-i] % m) * inva[K-1] % m 
    ans -= A[i] * tmp
    ans %= m

print(ans)