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())
lis = list(map(int, input().split()))
sort_lis = sorted(lis)
p = 10**9+7
fac_lis = [[0] for i in range(N)]
fac_lis[0] = 1
max_ans = 0
min_ans = 0

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

def combi(n,k):
  if n == k:
    return 1
  else:
    return fac_lis[n-1]*pow(fac_lis[k-1], p-2, p)*pow(fac_lis[n-k-1], p-2, p) % p

for i in range(K-1,N):
  max_ans += sort_lis[i]*combi(i, K-1)
  max_ans %= p
  
for i in range(N-K+1):
  min_ans += sort_lis[i]*combi(N-(i+1), K-1)
  min_ans %= p

ans = (max_ans - min_ans) % p
print(ans)