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
def modinv2(a,m):
    return pow(a,m-2,m)

N,K = map(int,input().split())
A = list(map(int,input().split()))
A.sort()
P = 10**9+7

cominv = [0 for i in range(N-1)]
for i in range(N-1):
    if i+2 == K:
        cominv[i] = 1
    elif i+1 == K:
        cominv[i] = (i+1)%P
    elif i+1 > K:
        a = modinv2(i-K+2,P)
        cominv[i] = cominv[i-1]*(i+1)*a%P

#print(cominv)
ans = 0

for i in range(N):
    if i <= N-K:
        b = A[i]*cominv[N-i-2]%P
        ans = (ans-b+P)%P
    if i >= K-1:
        c = A[i]*cominv[i-1]%P
        ans = (ans+c)%P

print(ans)
