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,K=map(int,input().split())
alist=list(map(int,input().split()))
alist.sort()
#print(alist)

inv_table = [0]+[1]
for i in range(2,N+1):
  inv_table.append(-(MOD//i)*inv_table[MOD%i]%MOD)

min_s,max_s=0,0
old_comb,new_comb=0,1
for i in range(K,N+1):
  #print(K,i,new_comb-old_comb)
  min_s+=(new_comb-old_comb)*alist[-1-(i-1)]
  min_s%=MOD
  max_s+=(new_comb-old_comb)*alist[i-1]
  max_s%=MOD
  
  old_comb=new_comb
  new_comb=old_comb*(i+1)*inv_table[i+1-K]%MOD
#print(min_s,max_s)

print((max_s-min_s)%MOD)