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 = [int(i) for i in input().split()]
a.sort()
mod = 10 ** 9 + 7
ans = 0

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

def combination(n, r):
    if (n != 0) & (n >= r):
        return f[n] * inv[r] * inv[n - r] % mod
    return 0    
    
ans = 0
for index, value in enumerate(a):
    ans += (combination(index, k - 1) - combination(n - index - 1, k - 1)) * value
print(ans % mod)