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, *a = map(int, open(0).read().split())
a.sort()

mod = 10 ** 9 + 7

fact = [1] * (n + 1)
for i in range(1, n + 1):
    fact[i] = fact[i - 1] * i % mod


def inv(x):
    return pow(x, mod - 2, mod)


def c(n, k):
    return fact[n] * inv(fact[n - k] * fact[k] % mod) % mod


ans = 0
for i in range(k - 1, n):
    # a[i]がmax
    ans += a[i] * c(i, k - 1) % mod
a = list(reversed(a))
for i in range(k - 1, n):
    ans -= a[i] * c(i, k - 1) % mod
print((ans + mod) % mod)
