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
MOD = 10**9+7

N,K = map(int,input().split())
A = list(map(int,input().split()))
A.sort()

ans = 0

numer = [0 for _ in range(N+1)]
numer[0] = 1
inv = [0 for _ in range(N+1)]
inv[0] = 1

for i in range(N):
    numer[i+1] = numer[i]*(i+1)%MOD

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

for i in range(N-K+1):
    ans += (A[N-i-1]-A[i])*numer[N-i-1]*inv[K-1]*inv[N-i-1-K+1]%MOD

print(ans%MOD)
