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

fac=[1]*(N+1)
inv=[1]*(N+1)
invfac=[1]*(N+1)
for i in range(2,N+1):
    fac[i]=fac[i-1]*i%MOD
    inv[i]=MOD-inv[MOD%i]*(MOD//i)%MOD
    invfac[i]=invfac[i-1]*inv[i]%MOD

A.sort()
ans=0
for l in range(N):
    r=N-l-1
    #max
    if l>=K-1:
        ans+=A[l]*fac[l]*invfac[l-K+1]*invfac[K-1]%MOD
    #min
    if r>=K-1:
        ans-=A[l]*fac[r]*invfac[r-K+1]*invfac[K-1]%MOD
    ans%=MOD

print(ans)
