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
def COMint():
  fac[0]=1
  fac[1]=1
  finv[0]=1
  finv[1]=1
  inv[1]=1
  for i in range(2,N+1):
    fac[i] = fac[i - 1] * i % MOD
    inv[i] = MOD - inv[MOD%i] * (MOD // i) % MOD
    finv[i] = finv[i - 1] * inv[i] % MOD
def com(n,k):
  if n<k:
    return 0
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD
MOD=10**9+7
N,K=[int(x) for x in input().split()]
A= [int(x) for x in input().split()]
A= sorted(A)
fac=[0]*(N+1)
inv=[0]*(N+1)
finv=[0]*(N+1)
COMint()
ans=0
#print(fac)
for j in range(N):
  ans+=(A[j])*com(j,K-1)
  ans-=(A[j])*com(N-1-j,K-1)
print(ans%(10**9+7))