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(map(int, input().split()))
A.sort()

p = 10**9 + 7
 
fac = [0] * (N + 33)
inv = [0] * (N + 33)
finv = [0] * (N + 33)

fac[0] = fac[1] = 1
inv[1] = 1
finv[0] = finv[1] = 1
 
for i in range(2, N+33):
  fac[i] = fac[i-1] * i % p
  inv[i] = p - inv[p%i] * (p // i) % p
  finv[i] = finv[i-1] * inv[i] % p

def comb(n, k):
  return fac[n] * finv[k] * finv[n-k] % p

ans = 0
ansm = 0

for i in range(K-1, N):
  ans = (ans + A[i] * comb(i, K-1)) % p

for i in range(N-K, -1, -1):
  ansm = (ansm + A[i] * comb(N-i-1, K-1)) % p

print((ans-ansm)%p)
