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()
MOD = 10**9+7

#c[i] := (i)C(K-1)
c = [0] * (N+1)
#frac[i] = i!%MOD
frac = [1] * (N+1)
for i in range(1, N+1):
  frac[i] = (frac[i-1]*i)%MOD
for i in range(1, N+1):
  if(i >= K-1):
    c[i] = frac[i]*pow(frac[K-1], MOD-2, MOD)*pow(frac[i-K+1], MOD-2, MOD)%MOD

  
ans = 0
for i in range(N):
  ans = (ans + A[i]*c[i])%MOD
for i in range(N):
  ans = (ans - A[i]*c[N-i-1])%MOD
  
print(ans)