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())
a=list(map(int,input().split()))

a.sort(reverse=True)


fact = [1]
fact_inv = [1]
mod=10**9+7
for i in range(10**5+1):
    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

  
c=[]
for i in range(1,n-k+1+1):
  c.append(mod_comb_k(n-i,k-1,MOD))
lc=len(c)
#print(c,a)
sum=0
for i in range(lc):
  sum+=c[i]*(a[i]-a[-i-1])%MOD
  
print(sum%MOD)
