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()))
a.sort()

mod=10**9+7
fcl=[1]*(n+1)
for i in range(1,n+1):
  fcl[i]=(fcl[i-1]*i)%mod
def comb(x,y,p):
  return ((fcl[x]*pow(fcl[y],p-2,p))%mod*pow(fcl[x-y],p-2,p))%mod

maxs=0
for i in range(k,n+1):
  maxs+=a[i-1]*comb(i-1,k-1,mod)
  maxs%=mod
mins=0
for i in range(n-k+1):
  mins+=a[i]*comb(n-i-1,k-1,mod)
  mins%=mod
ans=(maxs-mins)%mod
print(ans+mod if ans<0 else ans)