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 cmb(a,b,c):
    b = min(b,a-b)
    num = 1
    for i in range(b):
        num = num*(a-i) % c
    den = 1
    for i in range(b):
        den = den*(i+1) % c
    return num * pow(den,c-2,c) % c
mod = 10**9 + 7
n,k = map(int,input().split())
inv = [0,1]
for i in range(2,n):
  inv += [inv[mod % i]*(mod - mod//i) % mod]
a = list(map(int,input().split()))
a.sort()
ans = 0
c = 1
x = 1
if k == 1:
    print(0)
    exit()
for i in range(n-k+1):
    ans -= a[n-k-i] * c
    ans += a[k+i-n-1] * c
    ans %= mod
    c = c*(i+k)*inv[i+1] % mod
if ans < 0:
    ans += mod
print(ans)