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
def inv(x):
  y = 1
  while x != 1:
    y *= mod // x + 1
    x -= mod % x
    y %= mod
  return y

d = []
tmp = 1
for i in range(1,k):
  tmp *= n-i
  tmp %= mod
  tmp *= inv(k-i)
  tmp %= mod
d.append(tmp)
#print(tmp)
for i in range(1,n):
  tmp = d[-1]
  tmp *= inv(n-i)
  tmp %= mod
  tmp *= n-k+1-i
  tmp %= mod
  d.append(tmp)
#print(d)
ans = 0
for i in range(n):
  ans += d[i] * a[-i-1]
  ans -= d[i] * a[i]
  ans %= mod
print(ans)