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
#151_E
n, k = map(int, input().split())
a = sorted(list(map(int, input().split())))
mod = 10 ** 9 + 7

f = [1 for _ in range(n)]
f_inv = [1 for _ in range(n)]
for i in range(2, n):
    f[i] = (f[i-1] * i) % mod
    f_inv[i] = pow(f[i], mod-2, mod)
def comb(n,k):
    return f[n]*f_inv[k]*f_inv[n-k]%mod   
ans = 0
for i in range(n-k+1):
    ans = (ans + comb(n-i-1, k-1) * (a[-i-1]-a[i]))%mod
print(ans)