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 = list(sorted(list(map(int, input().split()))))
mod = 1000000007
fact = [1]
for i in range(1,n+1):
  fact.append((fact[-1] * i)%mod)
res = 0
for i in range(k-1, n):
  cnt = (a[i]*fact[i])%mod
  cnt = (cnt*pow(fact[k-1], mod-2, mod))%mod
  cnt = (cnt*pow(fact[i-k+1], mod-2, mod))%mod
  res = (res + cnt)%mod
  cnt = (a[n-i-1]*fact[i])%mod
  cnt = (cnt*pow(fact[k-1], mod-2, mod))%mod
  cnt = (cnt*pow(fact[i-k+1], mod-2, mod))%mod
  res = (res - cnt + mod)%mod
print(res)
