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()
if k == 1:
  print(0)
else:
  mod = 10 ** 9 + 7
  use = 1
  def inv(x):
    y = 1
    while x != 1:
      y *= mod // x + 1
      y %= mod
      x -= mod % x
    return y
  b = [0 for _ in range(n)]
  c = [1]
  for i in range(n-k):
    tmp = c[-1]
    tmp *= inv(i+1)
    tmp %= mod
    tmp *= i+k
    c.append(tmp)
  c.reverse()
  #print(c)
  for i in range(n-k+1):
    b[i] -= c[i]
    b[-i-1] += c[i]
  #print(b)
  ans = 0
  for i in range(n):
    ans += b[i] * a[i]
    ans %= mod
  print(ans)