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=[int(s) for s in input().split()]
ls=[int(s) for s in input().split()]
ls.sort()

MAX = N+1
fac = [1, 1]
finv = [1, 1]
inv = [0, 1]
for i in range(2, MAX):
  fac.append(fac[i - 1] * i % MOD)
  inv.append(MOD - inv[MOD % i] * (MOD // i) % MOD)
  finv.append(finv[i - 1] * inv[i] % MOD)
 
def COM(n, k):
  if n < k: 
    return 0
  if n < 0 or k < 0:
    return 0
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD

m=0
M=0
for i in range(N-K+1):
  m+=ls[i]*COM(N-i-1,K-1)%MOD
  M+=ls[-1-i]*COM(N-i-1,K-1)%MOD

print((M-m)%MOD)

