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 = (int(x) for x in input().split())
a = [int(x) for x in input().split()]
a = sorted(a)
MOD = 1000000007
fact = [1]
for i in range(1, n + 1):
    fact.append(fact[-1] * i % MOD)
def inv(i):
    return pow(fact[i], MOD - 2, MOD)
def max_min_a():
    a_sum = 0
    for i in range(k - 1, n):
        a_sum += a[i] * fact[i] * inv(i - k + 1) * inv(k - 1) % MOD
    return a_sum
max_a = max_min_a()
a = a[::-1]
min_a = max_min_a()
print(int((max_a - min_a) % MOD))