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()))
mod = 10**9+7

if K==1:print(0)
else:
  factorial=[1 for i in range(N+1)]
  for i in range(1,N+1):
    if i==1:factorial[i]=1
    else:factorial[i] = factorial[i-1]*i % mod
  
  def comb(n,k):
    return factorial[n]*pow(factorial[n-k]*factorial[k], -1, mod)

  A1=sorted(A)
  A2=A1[::-1]
  
  ans=0
  for i in range(N-K+1):
    ans += (A2[i]-A1[i])*comb(N-i-1,K-1)
  ans %= mod

  print(ans)