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
fac = [1, 1]
finv = [1, 1]
inv = [0, 1]

ans = 0

def comb(n, r):
  if n >= r:
    return fac[n] * ( finv[r] * finv[n-r] % mod ) % mod
  else:
    return 0
 
for i in range(2, N + 1):
  fac.append( ( fac[-1] * i ) % mod )
  inv.append( mod - ( inv[mod % i] * (mod // i) % mod ) )
  finv.append( finv[-1] * inv[-1]  % mod )

if K == 1:
  print(0)
else:
  for i, x in enumerate(A):
    cnt = x * ( comb(i, K-1) - comb(N-1-i, K-1) ) % mod
    ans += cnt
    ans %= mod
  print(ans)