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
fact = [1]
fact_inv = [1]
for i in range(10**5):
  new_fact = fact[-1]*(i+1)%mod
  fact.append(new_fact)
  fact_inv.append(pow(new_fact,mod-2,mod))

def mod_comb_k(n,k,mod):
  return fact[n]*fact_inv[k]%mod*fact_inv[n-k]%mod

N,K = map(int,input().split())
arr = list(map(int,input().split()))
arr = sorted(arr)
_max = 0
_min = 0
for i in range(K-1,N):
  _max += arr[i]*mod_comb_k(i,K-1,mod)
  _min += arr[i-K+1]*mod_comb_k(N-i+K-2,K-1,mod)
print((_max-_min)%mod)