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_MAX = 10**5+1
fact = [1] * N_MAX
for i in range(1,N_MAX):
  fact[i] = (fact[i-1]*i) % mod
  
def nCr(n,r):  
  if n < r:
    return 0
  return (fact[n] * pow(fact[r]*fact[n-r] ,mod-2,mod))% mod

n,k = map(int,input().split())
A = sorted(list(map(int,input().split())))

mi = 0
ma = 0

for i in range(1,n):
  m = nCr(n-i,k-1)
  mi += A[i-1] * m
  ma += A[-i]  * m
  
print((ma - mi)%mod)