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 = list(map(int,input().split()))

A = list(map(int,input().split()))

A.sort()

mod = 10**9 + 7

pow_list = [1,1]
p = 1

for i in range(2,N+1):
    p*=i
    p%=mod
    pow_list.append(p)

ans = 0

K_inv =  pow(pow_list[K-1],mod-2,mod)

#print(K_inv)

for i in range(N-K+1):
    coef = A[N-i-1] - A[i] + mod
    comb = pow_list[N-i-1] * pow(pow_list[N-K-i],mod-2,mod)
    comb%=mod
    comb*=K_inv
    comb%=mod
    ans += coef*comb
    ans %= mod

print(ans)