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
MOD = 1000000007

N,K = map(int,input().split())
A = list(map(int,input().split()))
A.sort()

step =[1]*(N+1)
for i in range(1,N+1,1):
    step[i]= (step[i-1]*i)%MOD
def nCk(n,k):
    return (step[n]*pow(step[k],MOD-2,MOD)*pow(step[n-k],MOD-2,MOD))%MOD

max_sum=0
min_sum=0
for i in range(0,N,1):
    if i+1 < K:
        continue
    max_sum += (A[i]*nCk(i,K-1) + MOD)%MOD
    min_sum += (A[N-1-i]*nCk(i,K-1) + MOD)%MOD

print((max_sum-min_sum)%MOD)


    