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 = int(1e+9 + 7)
a = sorted(a)

kai = [1]*(n+1)
gyaku = [1]*(n+1)

for i in range(2, n+1):
    kai[i] = kai[i-1]*i % mod
    gyaku[i] = gyaku[i-1]*pow(i, mod-2, mod) %mod

answer = 0
for i in range(k-1,n):
    answer = (answer + a[i] * kai[i] * gyaku[(i)-(k-1)] * gyaku[k-1]) % mod

answer2 = 0
for i in range(n-k+1):
    answer2 = (answer2 + a[i] * kai[n-i-1] * gyaku[(n-i)-k] * gyaku[k-1]) % mod


if k == 1:
    print(0)
else:
    print((answer - answer2)%mod)
