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=map(int, input().split())
A=list(map(int, input().split()))
A.sort()

upp=[1]*(N+1)
for i in range(2, N+1):
  upp[i]=upp[i-1]*i
  upp[i]%=MOD
  
inv=[1]*(N+1)
inv[N]=pow(upp[N], MOD-2, MOD)
for i in range(N, 1, -1):
  inv[i-1]=inv[i]*i
  inv[i-1]%=MOD
  
def modcomb(n, k):
  out=upp[n]*inv[n-k]%MOD
  out=out*inv[k]%MOD
  return out

tasu=0
hiku=0
  
for i in range(N):
  if N-i-1>=K-1:
    hiku+=A[i]*modcomb(N-i-1, K-1)
    hiku%=MOD
  if i>=K-1:
    tasu+=A[i]*modcomb(i, K-1)
    tasu%=MOD

print((tasu-hiku)%MOD)