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
#E
N,K=map(int,input().split())
A=list(map(int,input().split()))
mod=10**9+7
ans=0

fact=[1 for i in range(N+1)]
for i in range(2,N+1):
    fact[i]=(fact[i-1]*i)%mod
    
fact_inv=[1 for i in range(N+1)]
for i in range(2,N+1):
    fact_inv[i]=pow(fact[i],mod-2,mod)

def nCk(n,k):
    re=(fact[n]*fact_inv[n-k]*fact_inv[k])%mod
    return re

ans=0
A=sorted(A)
for i in range(K-1,N):
    ans+=nCk(i,K-1)*(A[i]-A[N-i-1])
    ans%=mod
    
print(ans)