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 # 変える
fac = [1]*n
finv = [1]*n
inv = [0]*n
inv[1] = 1
for i in range(2,n):
    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 comb(n,k):
    if n<k:
        return 0
    if n<0 or k<0:
        return 0
    return fac[n]*(finv[k] * finv[n-k] % mod)%mod
ans=0
for i in range(n-k+1):
    ans+=comb(n-i-1,k-1)*(a[n-i-1]-a[i])
print(ans%mod)