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
import sys
read = sys.stdin.read

n, k, *alst = map(int, read().split())
alst.sort()
lst1 = alst[k - 1:]
lst2 = alst[n - k::-1]
mod = 10 ** 9 + 7
res = 0
prep = 1
for i in range(n - k + 1):
    res += prep * (lst1[i] - lst2[i])
    res %= mod
    prep = prep * (i + k) * pow(i + 1, mod - 2, mod)
    prep %= mod

print(res)