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

f = [i for i in range(N+1)]
for i in range(2, N+1):
    f[i] *= f[i-1]
    f[i] %= mod
f[0] = 1

q = K - 1
fk = pow(f[q], mod - 2, mod)

total = 0

for i in range(N - K + 1):
    p = N - i - 1

    c = (f[p] * fk * pow(f[p-q], mod-2, mod)) % mod
    total += c * (A[-1 - i] - A[i])
    total %= mod

print(total)
