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()))
A.sort()
MOD = 10**9+7

def combinations_count(n, r):
    if n >= r:
        return ((fact[n] * fact_inv[n-r])%MOD) * fact_inv[r]%MOD
    else:
        return 0

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

ans = 0
L = len(A)
for i,a in enumerate(A):
    MIN = combinations_count(L-1-i,K-1)
    MAX = combinations_count(i,K-1)
    ans += MAX*a - MIN*a
    ans %= MOD

print(ans)