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

FAC = [1]
INV = [1]
for i in range(1,N+1):
  FAC.append((FAC[i-1]*i) % MOD)
  INV.append(pow(FAC[-1],MOD-2,MOD))
def nCr(n,r):
  return FAC[n]*INV[n-r]*INV[r]

if N == 1:
  print(0)
  exit()
ans = 0
for i in range(N):
  if i >= K-1:
    ans += nCr(i,K-1)*A[i]
    ans %= MOD
  if N-i-1 >= K-1:
    ans -= nCr(N-i-1,K-1)*A[i]
    ans %= MOD
print(ans)