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())
arr=list(map(int,input().split()))
arr=sorted(arr)
acum=[0]
for i in range(n):
  acum.append(acum[-1]+arr[i])
mod=10**9+7
ans=0
if k==1:
  print(ans)
elif k==2:
  for i in range(1,n):
    ans+=acum[n]-acum[i]-arr[i-1]*(n-i)
    ans%=mod
  print(ans)
else:
  facts=[1,1]
  for i in range(2,n-1):
    facts.append(facts[-1]*i)
    facts[-1]%=mod
  for i in range(k-1,n):
    ways=facts[i-1]*pow(facts[k-2],mod-2,mod)*pow(facts[(i-1)-(k-2)],mod-2,mod)
    ways%=mod
    ans+=(acum[n]-acum[i]-acum[n-i])*ways
    ans%=mod
  print(ans)