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()))
mod=10**9+7
a.sort()
mx=10**5+1
fac=[0]*mx
finv=[0]*mx
inv=[0]*mx
fac[0]=fac[1]=1
finv[0]=finv[1]=1
inv[1]=1
for i in range(2,mx):
  fac[i]=(fac[i-1]*i)%mod
  inv[i]=mod-(inv[mod%i]*(mod//i))%mod
  finv[i]=(finv[i-1]*inv[i])%mod
comb=lambda a,b:(fac[a]*finv[b]*finv[a-b])
minX=0
maxX=0
for i in range(n-k+1):
  minX+=a[i]*comb(n-i-1,k-1)
for i in range(k-1,n):
  maxX+=a[i]*comb(i,k-1)
print((maxX-minX)%mod)