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
kaidan=[1]*(n+3)
gyaku=[1]*(n+3)
for i in range(n+2):
    kaidan[i+1]=(i+1)*kaidan[i]%mod
for i in range(n+2):
    gyaku[i+1]=pow(kaidan[i+1], mod-2,mod)
def comb(n,r):
    if r>=0 and n-r>=0:
        return kaidan[n]*gyaku[n-r]*gyaku[r]%mod
    else:
        return 0
A.sort()
R=list(reversed(A))
ans=0
for i in range(n-k+1):
    ans-=A[i]*comb(n-1-i,k-1)
    ans+=R[i]*comb(n-1-i,k-1)
print(ans%mod)