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 = sorted(A)

MOD= 10**9+7

f = [1]*(n+1)
inv = [1]*(n+1)

for i in range(1, n+1):
  f[i] = f[i-1]*i%MOD
  
inv[n] = pow(f[n], MOD-2, MOD)
for i in range(n-1, 0, -1):
  inv[i] = inv[i+1]*(i+1)%MOD

def nCr(n, r):
  return f[n]*inv[n-r]%MOD*inv[r]%MOD
    
ans = 0
for i in range(n):
  if i+1<k:
    continue
  cnt = nCr(i, k-1)
  ans += cnt*A[i]%MOD
  ans %= MOD
  
for i in range(n-1, -1, -1):
  if n-i<k:
    continue
  cnt = nCr(n-i-1, k-1)
  ans -= cnt*A[i]%MOD
  ans %= MOD
  
print(ans)