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())
sortedList = sorted(list(map(int, input().split())))
mod = 10 ** 9 + 7

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

def cmb(n, k):
  return factorial[n] * pow(factorial[n - k], mod - 2, mod) * pow(factorial[k], mod - 2, mod)

result = 0
for i in range(1, n - k + 2):
  val = cmb(n - i, k - 1) * (sortedList[n - i] - sortedList[i - 1])
  result += val
print(result % mod)
