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())
aa = list(map(int, input().split()))

aa.sort()
mod = 10 **9 +7
fac = [1] * 100000
inv = [1] * 100000
for i in range(1,len(fac)):
    fac[i] = fac[i-1] * i % mod
    inv[i] = pow(fac[i], mod-2, mod)
    
def combi(m, j):
    if j > m:
        return 0
    return (fac[m] * inv[m-j] * inv[j]) % mod


ret = 0
for i, a in enumerate(aa):
    n_max = combi(i, k-1)
    n_min = combi(n - 1 - i, k-1)
    ret = (ret + (n_max - n_min) * a) % mod
print(ret)